=
Insight number 2: to evaluate the limit of a:
1. Rational function: you can factorize and cancel out what you can
2. Radicals (subtractions of square roots): multiply and divide by the
conjugate. For example:
Vx2 + 1 - x
x? +1 - x2
x2 +1-x=
(V x2 +1 + x)
Vx2 + 1 + x
V.x2 + 1 + x
1
Vx2 +1 + x
3. Trigonometric functions: try to connect your limit with important
sin (x)
trigonometric limits like limx40 = 1
If you are stuck with a trig limit, express all the trig functions in terms
of sine and cosine.
4. If you are composing continuous functions, you can pass the limit
inside the external function: Cimz-a f(g(x)) = f(lim,-a 9(x))

Answer: (5/8)x

Step-by-step explanation:

Compute the first few derivatives to reveal a pattern:

f(x) = x sin(x)

f '(x) = x cos(x) + sin(x)

f ''(x) = (-x sin(x) + cos(x)) + cos(x) = -x sin(x) + 2 cos(x)

f '''(x) = (-x cos(x) - sin(x)) - 2 sin(x) = -x cos(x) - 3 sin(x)

f ''''(x) = (x sin(x) - cos(x)) - 3 cos(x)) = x sin(x) - 4 cos(x)

f ⁽⁵⁾(x) = (x cos(x) + sin(x)) + 4 sin(x) = x cos(x) + 5 sin(x)

f ⁽⁶⁾(x) = (-x sin(x) + cos(x)) + 5 cos(x) = -x sin(x) + 6 cos(x)

f ⁽⁷⁾(x) = (-x cos(x) - sin(x)) - 6 sin(x) = -x cos(x) - 7 sin(x)

f ⁽⁸⁾(x) = (x sin(x) - cos(x)) - 7 cos(x) = x sin(x) - 8 cos(x)

and so on.

The pattern should be clear: for some integer k,

• if n = 4k, then f ⁽ⁿ ⁾(x) = x sin(x) - n cos(x)

• if n = 4k + 1, then f ⁽ⁿ ⁾(x) = x cos(x) + n sin(x)

• if n = 4k + 2, then f ⁽ⁿ ⁾(x) = -x sin(x) + n cos(x)

• if n = 4k + 3, then f ⁽ⁿ ⁾(x) = -x cos(x) - n cos(x)

80 is a multiple of 4, so the 80th derivative falls in the first category. Then

f ⁽⁸⁰⁾(x) = x sin(x) - 80 cos(x)

Answer:

x = 10√3

y = 10

Step-by-step explanation:

Step 1:

x = r·cos(30°)

y = r·sin(30°)

Step 2:

x = 20·√3/2 = 10√3

y = 20·1/2 = 10

However, there is a shortcut. Since there is a hypotenuse, there is a 90° angle. You are given a 30° angle, so the triangle is 30°-60°-90°.

The sides of a 30°-60°-90° triangle are in the ratio 1:√3:2.

The side opposite the 90° angle has length 20, so the side opposite the 30° angle has length 10, and the side opposite the 60° angle has length 10√3.

Answer:

You need to include a picture because there is no figure. I don't know the other numbers of the angles orsides.

Step-by-step explanation:

Answer: 252

Step-by-step explanation:

Answer:

8900

Step-by-step explanation:

25 * 89 / [tex]\frac{1}{4}[/tex] = 25 * 89 * 4 = 100 * 89 = 8900

Answer:

Step-by-step explanation:

270 div

Answer:

y = 6x

Step-by-step explanation:

You can easily find the slope by using slope formula:

(y2-y1) / (x2-x1) (the numbers are subscript)

E.g: (24-12) / (4-2) = 12/2 = 6

m(slope) = 6

Hope this helped :)

(You can also check if it’s correct by inputting the coords into the equation, seeing if all solutions are aplicable).

Answer:

The first choice is the right answer.

Step-by-step explanation:

Y = 3x+7

First choice

y = 3(0) + 7 = 7

y = 3(1) + 7 = 10

y = 3(2) + 7 = 13

second choice

y = 3(7) + 7 = 28. output on table shows 0

third choice

y = 3(0) + 7 = 7

y = 3(1) + 7 = 10 doesn't work as y output in third choice says 8

fourth choice.

y = 3(7) + 7 = 28 output on table shows 0

Answer:

2.5

Step-by-step explanation:

(I'm assuming you're doing this the same way I learned it, if not I'm sorry if it doesn't make sense)

[tex]\frac{2}{x}[/tex]=[tex]\frac{12}{15}[/tex]

Cross multiply

12x=30

Divide

x=2.5

This is just one way to do the problem. An easier way is to simplify the fractions.

[tex]\frac{2}{x}[/tex]=[tex]\frac{4}{5}[/tex]

You can either cross multiply or figure out that 2 is half of four and simply divide 5 by 2 which will also result in 2.5

Answer:

$18.92

Step-by-step explanation:

20-1.08=18.92

Answer:

$18.92

Step-by-step explanation:

Subtract $1.08 from $20

18.92

So Ravi should get $18.92 back

Hope this helps :)

Answer:

No, because 2(3x-5)=6x-10, and 6x-10 is not equal to 6x-8

Step-by-step explanation:

Answer:

1/20

Step-by-step explanation:

1/5 chance she will wear the blue shirt on the first day and 1/4 chance she will wear a grey shirt on the second day.

1/5 X 1/4 = 1/20

Answer:

i got 1/20 as my answer

Answer:

30$ for 15 cans of coffee.

Step-by-step explanation:

$12 for 6 cans of coffee

12 divided by 6 = 2

$2 per can of coffee

15 cans of coffee times $2 = 30$

Hope this helps

Answer:

(6, 687)

Step-by-step explanation:

Answer:

not understanding meaning of your question

Step-by-step explanation:

sooooooooooooorrrrrrrrrrrrrrrrrryy

Answer:

A im pretty sure

Step-by-step explanation:

Answer:

how much money is he saving????

Step-by-step explanation:

Answer:

6 Students

Step-by-step explanation:

10% of 60 is 6.

Answer:

4

Step-by-step explanation:

The factors of 4 are: 1, 2, 4

The factors of 12 are: 1, 2, 3, 4, 6, 12

Then the greatest common factor is 4.

Hope this helps! :D

Please mark brainlist

Answer:

4y

Step-by-step explanation:

I just took it in my math period,

Answer:

Both functions are increasing on all intervals of x: True

Both functions have the same y intercept: True

Both functions approach the same value as x approaches infinity: True

Both functions approach negative infinity as x approaches negative infinity: True.

The functions have the same x intercept: False, they have no x intercept.

Step-by-step explanation:

f(x) is stated to be an exponetial function, hence

[tex]f(x)=ab^{x}[/tex]

f(0) is given as -12, so

-12=a

f(1) is given as -4, so

-4=-12b

b=1/3

This implies that

[tex]f(x)=-12(\frac{1}{3})^{x}[/tex]

g(x) is stated to be

[tex]g(x)=-12(\frac{1}{3})^{x}[/tex]

Conclusion: the functions are identical.

Answer:

so the answers are

the functions have the same y-intercept

both functions approach negative infinity as x approaches infinity

both functions are increasing on all intervals of x

Answer:

y = 40

Step-by-step explanation:

Given, y = 5 * 2^x

If x = 3, y would be:

Substitute the value of x into the given function.

Thus,

y = 5*2³

y = 5*8

y = 40

Answer:

1. x = 65

2. x = 40

3. x = -7

4. x = -4

5. x = -7

6. x = 4

Step-by-step explanation:

Angles in a triangle always add up to 180 degrees.

Thus, for each triangle you can write an equation setting the sum of the three angles equal to 180, and solving for x.

1. 180 = 80 + 35 + x

   180 - (80 + 35) = x

   180 - 115 = x

   65 = x

2. 180 = 70 + 70 + x

   180 - (70 + 70) = x

   180 - 140 = x

   40 = x

3.  180 = 76 + 41 + (x+ 70)

    180 - (76 + 41) = x + 70

    180 - 117 = x + 70

    63 = x + 70

    63 - 70 = x

    -7 = x    

4. (the red square means its a right angle = 90 degrees)

   180 = 90 + 25 + (x + 69)

   180 - (90 + 25) = x + 69

   180 - 115 = x + 69

   65 = x + 69

   65 - 69 = x

   x = -4

5. 180 = 50 + (57 +x) + (x + 87)

   180 - 50 = (57 +x) + (x + 87)

    130 = (57 +x) + (x + 87)

  combine like terms

  130 =  144 + 2x  

  130 - 144 = 2x

  -14 = 2x

   -7 = x

6. 180 = 80 + (9x + 4) + (16x - 4)

   180 - 80 = (9x + 4) + (16x - 4)

   100 = (9x + 4) + (16x - 4)

   combine like terms

    100 = 25x + 0

    100 = 25x

    4 = x