Question 1

Evaluate $$\lim_{x 	o 2^-} (f(x) - g(x))$$ using the graphs provided in the second image.

Accepted Answer

$$-1$$

Question 2

Using the graphs in the second image, what is $$f(2) + g(2) + \lim_{x 	o -1} g(x)$$?

Accepted Answer

$$2$$

Question 3

Given the function $$f(x) = \ln(x^2$ + 1)$$, what is $$f''(x)$$?

Accepted Answer

$$\frac{-2x^2$+2}{(x^2$+1)^2$$}$

Question 4

Find the derivative of $$y = x \sin x.$$

Accepted Answer

$$\sin x + x \cos x$$

Question 5

Evaluate $$\lim_{x 	o 0} \frac{\sin(3x)}{x}.$$

Accepted Answer

$$3$$

Question 6

If $$f(x) = x^2$ e^x$$, what is $$f'(x)$$?

Accepted Answer

$$e^x (2x + x^2$)$$

Question 7

Evaluate $$\$$int_0$$^1 (3x^2$ + 2x) dx.$$

Accepted Answer

$$\frac{5}{2}$$

Question 8

Find the area enclosed between $$y(x) = x^2$ + 3$$ and the x-axis on $$[0, 2].$$

Accepted Answer

$$\frac{26}{3}$$

Question 9

Let $$f(x) = \frac{2x^2$}{x^2$ - 4}. $$What are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 10

A circular ripple is expanding in a pond so that its radius increases at a rate of $$2 cm/s. $$How fast is the area of the circle increasing when the radius is $$5 cm$$?

Accepted Answer

$$20\pi cm$^2/s$$

Question 11

A $$10-ft $$ladder is leaning against a vertical wall. The bottom of the ladder is sliding away from the wall at a rate of $$3 ft/s. $$How fast is the top of the ladder sliding down the wall when the bottom is $$6 ft $$from the wall?

Accepted Answer

$$1.8 ft/s$$

Question 12

Evaluate $$\$$int_0$$^1 (e^x + \sqrt{x}) dx.$$

Accepted Answer

$$e - 1 + \frac{2}{3}$$

Question 13

Let $$F(x) = \$$int_0$$^x \arccos t \, dt. $$Use the Fundamental Theorem of Calculus to find $$F'(x).$$

Accepted Answer

$$\arccos x$$

Question 14

Given $$f(x) = x^3$ - 3x^2$ + 2$$, find the critical points.

Accepted Answer

$$x = 0, x = 2$$

Question 15

Evaluate $$\$$int_0$$^2 x e$$^{x^2}$$ dx.$$

Accepted Answer

$$\frac{1}{2}(e^4$ - 1)$$

Question 16

Let $$f(x) = 	an$$^{-1}$$(x - 1). $$What is $$f'(x)$$?

Accepted Answer

$$\frac{1}{1 + (x - 1)^2$}$$

Question 17

Find the linear approximation $$L(x) of$$ $$f(x) = e^x \cos x at$$ $$x = 0.$$

Accepted Answer

$$1 + x$$

Question 18

Evaluate $$\$$int_0$$^1 (u + 2)(u - 3) du.$$

Accepted Answer

$$-\frac{7}{6}$$

Question 19

Let $$f(x) = \frac{2x^2$}{x^2$ - 4}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 2, x 
eq -2$$

Guided Practice: Evaluating Limits Using Graphs

Guida di studio - Domande di pratica

Study guide - Flashcard