Please find the general limit of the following function:
[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]
Answers
Answer:
The general limit exists at x = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
[tex]\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))[/tex]
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))[/tex]Since the given function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300[/tex]
The right-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))[/tex]
Again, since the function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]=300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Thus, we can see that:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at x = 9 and is equal to 300.
Step-by-step explanation:
Hey there!
Please look your required answer in picture.
Note: In left hand limit always take a smaller near number of the approaching number. For example as in the solution I took the 8.99,8.999 as it is smaller than 9 but very near to it.
And in right hand limit always take a smaller and just greater near number than the approaching number. For example, I took 9.01,9.001 which a just greater but very near to 9.
Hope it helps!
![Please Find The General Limit Of The Following Function:[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/VXEkDv7kz8vh9qpxMdJg0pkGvnX4gJ0D.jpeg)
Related Questions
A furniture delivery truck leaves the store at 8 A.M. It travels 6 miles east, then 4 miles south, then 2 miles west and then 4 miles north.
At the end of this route, how far is the truck from the store?
Answers
Answer:
It's 4 miles East from the store.
Step-by-step explanation:
6 miles east - 2 miles west = 4 miles East
Displacement for north and south should cancel out since they are equal to each other.
Larissa dives into a pool that is 8 feet deep. She touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water.
What is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point?
36.9°
41.4°
48.6°
53.1°
Answers
Answer:
It would be 53.1
Step-by-step explanation:
Vote branlyist Please...
The approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point is; D: 53.1°
What is angle of elevation?We are told that she dived into the pool that was 8 ft deep.
She touches the bottom with her hands 6 ft horizontally.
Thus, a triangle is formed here with 8 being the opposite side of the angle of elevation and 6 being the adjacent side of the triangle.
Using trigonometric ratios, we can say that;
θ = tan⁻¹(8/6)
θ = 53.1°
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the height of a tower is 15m more than tiwce the height of a building find the height of the building if tower is 255m tall
Answers
Answer: 120m
Step-by-step explanation:
Let the height of the building be represented by x.
Since the height of a tower is 15m more than tiwce the height of a building, the height of the tower will be:
= (2 × x) + 15
= 2x + 15
Since the tower is 255m tall, therefore,
2x + 15 = 255
2x = 255 - 15
2x = 240
x = 240/2
x = 120
The height of the building is 120m
Simplify the radical completely.
Answers
Answer:
D
Step-by-step explanation:
But basically, one by one you try moving the terms out of the radical.
75 is also 25 * 3 and since 25 has a perfect square root of 5 that goes out and 3 stays inside the radical.
x^3 is also x^2 * x and since x^2 has a perfect square root which is just x that goes outside while the remaining x stays inside.
y^9 is also y^8 * y and since we move variables out the radical in twos y^ goes outside the radical and y stays inside alone.
Finally, z is just z it can't be taken out so it stays inside the radical.
Hope that helps!
Which statement about population parameters and point estimates is false? O A. o is the population standard deviation. It is usually unknown. B. p is the sample mean. It is used to estimate the population mean. C. sis the sample standard deviation. It is the square root of the variance. O D. nis the sample size. It is used to calculate the sample mean. SUBMIT
Answers
Using the Central Limit Theorem, the false statement is given by:
B. [tex]\mu[/tex] is the sample mean. It is used to estimate the population mean.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with population mean [tex]\mu[/tex] and population standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard error [tex]s_E = \frac{\sigma}{\sqrt{n}}[/tex].
If we have the standard deviation for the sample s, the Central Limit Theorem can also be applied.
The sample mean is given by [tex]\overline{x}[/tex], hence option B is false.
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What is the slope of the line below?
(-2,4) (5,4)
A. Positive
B. Zero
C. Undefined
D. Negative
Answers
Answer:
B
Step-by-step explanation:
the slope is 0
the y intercept is ( 0,4 )
What can you tell about a triangle when vibe three side lengths
Answers
Answer:All you have to do is use the Triangle Inequality Theorem, which states that the sum of two side lengths of a triangle is always greater than the third side. If this is true for all three combinations of added side lengths, then you will have a triangle.
Hope it helps...
The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards (according to GolfWeek). Assume that the driving distance for these golfers is uniformly distributed over this interval. a. Give a mathematical expression for the probability density function of driving distance. b. What is the probability the driving distance for one of these golfers is less than 290 yards
Answers
Answer:
a) [tex]f(x) = \frac{1}{25.9}[/tex]
b) 0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
The probability density function of the uniform distribution is:
[tex]f(x) = \frac{1}{b-a}[/tex]
The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards.
This means that [tex]a = 284.7, b = 310.6[/tex].
a. Give a mathematical expression for the probability density function of driving distance.
[tex]f(x) = \frac{1}{b-a} = \frac{1}{310.6-284.7} = \frac{1}{25.9}[/tex]
b. What is the probability the driving distance for one of these golfers is less than 290 yards?
[tex]P(X < 290) = \frac{290 - 284.7}{310.6-284.7} = 0.2046[/tex]
0.2046 = 20.46% probability the driving distance for one of these golfers is less than 290 yards
solve the inequality
2(4 x + 1)< 3 (2 x - 3)
Answers
Answer:
[tex]2 (4x + 1) < 3(2x - 3) \\8x + 2 < 6x -9 \\8x - 6x < -9 - 2\\2x < -11\\\\x< - \frac{11}{2}[/tex]
Answer:
x> - 11/2
Step-by-step explanation:
See image below:)
Identify the restrictions on the domain.
x+1x+9÷xx−4
x≠−1,4
x≠−9,4
x≠−1,0
x≠−9,0
[tex]Identify the restrictions on the domain. x+1x+9÷xx−4x≠−1,4x≠−9,4x≠−1,0x≠−9,0[/tex]
Answers
The distance that students drive to school is best modeled with a skewed right distribution that has a mean of 10 miles and a standard deviation of 2 miles. Suppose a sample of 100 students has been taken and the sample mean distance for the sample is calculated. Describe the shape of the sampling distribution of the sample mean
Answers
Answer:
The answer is "Approximately normal".
Step-by-step explanation:
sample size[tex]n=100[/tex]
Sample size [tex]n \geq 30[/tex]
It is because [tex]C \perp T[/tex] the sampling distribution of the sample means is approximately normal.
PLS HELP ASAP! FIND THE VOLUME OF THE GIVEN FIGURE.
Thank you
Answers
Answer:
120
Step-by-step explanation:
all you have to do is multiply the length, width, and height.
5x8=40
40x3=120
Hope this help!!!
Have a nice day!!!
In January 2013, a country's first-class mail rates increased to 52 cents for the first ounce, and 23 cents for each additional ounce. If Sabrina spent
$1742 for a total of 48 stamps of these two denominations, how many stamps of each denomination did she buy?
She bought
of the 52 cent stamps and
of the 23 cent stamps.
Answers
Answer:
She bought
22 of the 52 cent stamps and
26 of the 23 cent stamps.
Step-by-step explanation:
Given :
Total stamp increase = 48
Let number of 52 cent stamp = x
Number of 23 cent stamp = 48 - x
The cost equation :
0.52*x + 0.23*(48-x) = 17.42
0.52x + 11.04 - 0.23x = 17.42
0.52x - 0.23x = 17.42 - 11.04
0.29x = 6.38
x = 6.38 / 0.29
x = 22
Hence,
She bought 22 ; 52-cent stamps
And (48 - 22) = 26, 23-cent stamps
A candle is in the shape of a cylinder. The candle has a diameter of 6 inches and a height of 5 inches What is the volume of the candle? (Use 3.14
A. 94.2 cubic inches
B. 141.3 cubic inches
C. 150.7 cubic inches
D. 188.4 cubic inches
Answers
Determine the distance between points (x1, y1) and point (x2, y2), and assign the result to point Distance. The calculation is:
Answers
Given:
The two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
To find:
The distance between given points.
Solution:
Plot the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] randomly randomly on a coordinate plane, then form a right angle triangle as shown in the below figure.
Now, the hypotenuse is the distance between the two points.
[tex]\text{Perpendicular}=y_2-y_1[/tex]
[tex]\text{Base}=x_2-x_1[/tex]
Using Pythagoras theorem,
[tex]\text{Hypotenuse}^2=\text{Base}^2+\text{Perpendicular}^2[/tex]
[tex]d^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Taking square root on both sides, we get
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] [Distance is always positive]
Therefore, the distance between the two points is [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]. It is also known as distance formula.
Determine whether the function is linear or quadratic.
y = (x + 1)(8x - 8) - 8x2
a) Linear
b) Quadratic
Answers
Answer:
it's a linear
since when you expand the equation (x+1)(8x-8) the x is equal to zero which is left for y to be the subject
8x²-24= y
PLEASE HELP!!!!!!!!!!!!!!!!!!
Answers
Which of the following statements represents a correct relationship?
300 < 30
547 > 574
20,007 < 20,070
6,050 = 6,060
Answers
Can someone help me with this question
Answers
Answer:
The two minimum numbers = 5, 5
Step-by-step explanation:
Let the first number = x
let the second number = y
Their sum: x + y = 10
Sum of their squares: = x² + y²
y = 10 - x
f(x) = x² + (10 - x)²
f(x) = x² + 100 - 20x + x²
f(x) = 2x² - 20x + 100
Find the derivative of f(x), to obtain the critical points;
f'(x) = 4x - 20
4x - 20 = 0
4x = 20
x = 5
The value of y is calculated as;
y = 10 - x
y = 10 - 5
y = 5
The two minimum numbers = 5, 5
what is the answer
help
Answers
Answer: With that assumption, we have a square, whose area is given by the formula Asquare=a2, and two semicircles. The distance D is simply the square's diagonal. The area of each semicircle is given by the formula Asemicircle=π*r2/2. then you will get your answer!
PLEASE HELP FAST I NEED HELP WITH THIS!
Answers
Answer:
Step-by-step explanation:
13. Find the total number of coinsss
8+4+3+1
=16
First pick:
1/16
Second pick:
1/15
So I guess your chances are 1/16+1/15 ?
=31/240
hopefully
14.
add the sockss
3+4+3
= 10
First pick
1/10
Second Pick
1/9
Add them:
19/90
Forgive me if this is wrong
:,)
Which of the following is not equal to a ratio of 5 to 2?
A. 25: 10 C.35: 15
B. 35: 14 D. 40:16
Answers
Answer:
C 35:15
Step-by-step explanation:
because 35:15 =5:3 so it is not equal to a ratio of 5 is to 2
Answer:
C
Step-by-step explanation:
If you simplify all the ratios, then you get the following:
A. 25/5 : 10/5 = 5:2
B. 35/7 : 14/7 = 5:2
C. 35/5 : 15/5 = 7:3
D. 40/8 : 16/8 = 5:2
A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 3 inches, and a height of 3 1/2
inches. What is the surface area?
Answers
Answer:
[tex]Area = 138in^2[/tex]
Step-by-step explanation:
Given
[tex]L = 9; W =3; H =3\frac{1}{2}[/tex]
Required
The surface area
This is calculated as:
[tex]Area = 2(LW + LH + WH)[/tex]
So:
[tex]Area = 2(9*3 + 9*3\frac{1}{2} + 3*3\frac{1}{2})[/tex]
[tex]Area = 2(27 + 31\frac{1}{2} + 10\frac{1}{2})[/tex]
[tex]Area = 2*69[/tex]
[tex]Area = 138in^2[/tex]
Find the area of each sector. Round your answers to the nearest tenth.
Answers
Answer:
a = 117.3 cm²
Step-by-step explanation:
a = (1/2)∅r²
a = (1/2)(7π/6)(8²)
a = (1/2)(7 * 3.14159/6)(64)
a = 117.3 cm²
6!3! divided by 2!5!
Simplify the answer as much as possible.
Answers
Answer:
3/20
Step-by-step explanation:
Set up the quotient:
6!3!
------
2!5!
6! is equivalent to 6*5!, and so we have:
6*5!3! 6*5!3! 6*3*2*1 6
------------ which reduces to ------------- or ------------------- or ------------
2!5! 2!5! 2*5*4*3*2*1 (2)*5*4
3
This final result simplifies further to ---------------
20
A collection of 39 coins consists of dimes and nickels. The total value is $2.75. How many dimes and how many nickels are there?
Answers
Answer:
23 nickels and 16 dimes
Step-by-step explanation:
16 dimes = 1.60
23 nickels = 1.15
1.60 + 1.15 = 2.75
Find the value of the polynomial when x=1 and y=-2
Answers
Answer:
the answer is : ................
5
A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.
Answers
Answer:
20%
Step-by-step explanation:
vrrggrgrhreah
A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?
a. X1 + X2 + X3 + X4 = 1
b. X1 + X2 + X3 + X4 = 1
c. X1 + X2 + X3 + X4= 1
d. X1 + X2 + X3+ X4= 0
Answers
Given:
A company wants to select 1 project from a set of 4 possible projects.
Consider the options are:
a. [tex]X_1+X_2+X_3+X_4=1[/tex]
b. [tex]X_1+X_2+X_3+X_4\leq 1[/tex]
c. [tex]X_1+X_2+X_3+X_4\geq 1[/tex]
d. [tex]X_1+X_2+X_3+X_4\geq 0[/tex]
To find:
The constraints that ensures only 1 will be selected.
Solution:
It is given that the company wants to select 1 project from a set of 4 possible projects. It means the sum of selected projects must be equal to 1.
[tex]X_1+X_2+X_3+X_4=1[/tex]
Therefore, the correct option is (a).
What is Limit of (3 x minus 3) Superscript five-halves Baseline as x approaches 4
Answers
Answer:
d 243
Step-by-step explanation:
The solution of given function is 243
What is limit of function?
A limit defined as the value which a function approaches as that function's inputs get closer and closer to some number
[tex]lim\ (3x-3)^\frac{5}{2} \\x\to 4[/tex]
[tex](3(4)-3)^\frac{5}{2}[/tex]
[tex](12-3)^\frac{5}{2}[/tex]
[tex](9)^\frac{5}{2}[/tex]
[tex](3^2)^\frac{5}{2}[/tex]
[tex]3^5[/tex]
243
Hence, the solution of given function is 243
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