Question 1

Given the graph above, what is $$\lim\limits_{x 	o 1^-} f(x)$$?

Accepted Answer

$$-2$$

Question 2

Given the graph above, what is $$\lim\limits_{x 	o 1^+} f(x)$$?

Accepted Answer

$$1$$

Question 3

Given the graph above, what is $$f(1)$$?

Accepted Answer

$$-3$$

Question 4

At which $$x-$$values does $$f(x)$$ have a discontinuity?

Accepted Answer

$$x = 1$$ 	ext{ and } x = -1$

Question 5

Evaluate $$\lim\limits_{x 	o 2} \frac{x^3$ - 9}{x - 2}.$$

Accepted Answer

$$5$$

Question 6

Find the average rate of change of $$F(t)$$ from $$t = 1 to$$ $$t = 3$$ given $$F(1) = 12$$ and $$F(3) = 18.$$

Accepted Answer

$$3$$

Question 7

A car's position is given by $$s(t) = 6t. $$What is the average velocity from $$t = 0 to$$ $$t = 4$$?

Accepted Answer

$$12$$ feet per second

Question 8

Find the derivative of $$f(x) = 2x^5$ - 3x^2$ + 4.$$

Accepted Answer

$$10x^4 - 6x$

Question 9

Given $$h(t) = -16t^2$ + 40t + 100$$, what is the height of the ball after $$3$$ seconds?

Accepted Answer

$$76 ft$$

Question 10

Given $$h(t) = -16t^2$ + 40t + 100$$, what is the velocity of the ball after $$3$$ seconds?

Accepted Answer

$$-56 ft/sec$$

Question 11

Find the equation of the tangent line to $$f(x) = 3x^2$ - 5x + 8 at$$ $$x = 2.$$

Accepted Answer

$$y = 7x - 4$$

Question 12

Evaluate $$\lim\limits_{x 	o 0} \frac{\cos 3x - 1}{x}.$$

Accepted Answer

$$0$$

Question 13

Find the second derivative of $$y = x^2$ - 3x + 4.$$

Accepted Answer

$$2$$

Question 14

Given $$f(x) = 	an(2x)$$, find $$f''(x).$$

Accepted Answer

$$8\sec^2$(2x)	an(2x)$$

Question 15

Find the instantaneous rate of change in the number of people playing a game after 4 weeks, given $$g(t) = \frac{800}{t^2$ + 8}.$$

Accepted Answer

$$-11$$ people/week

Limits and Continuity from a Graph – Step-by-Step Guidance

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