10 multiple choice and 5 short answer calculus questions

1.

Use your graphing calculator to evaluate limit as x goes to infinity of the quantity 1 plus 2 times e raised to the x power all raised to the power of 1 divided by x . (5 points)


2.

Describe the discontinuity for the function f of x equals the quotient of the quantity x squared plus 25 and the quantity x minus 5 . (5 points)



3.

Find limit as x goes to 0 of the quotient of the sine of negative 6 times x and the sine of negative 5 times x . (5 points)



4.

Evaluate limit as x goes to negative 8 from the right of the quotient of x and the quantity x plus 8 . (5 points)



5.

Evaluate limit as x goes to infinity of the quotient of the negative 4 times x cubed plus 3 times x squared plus 6 times x and the quantity 6 times x squared minus 4 times x minus 5 . (5 points)



6.

Which of the following is the graph of which function has y = -3 as an asymptote? (5 points)



7.

If is continuous at x = -4, find f(-4). (5 points)



8.

Where is f of x equals the quotient of the quantity x minus 3 and x squared plus 2 times x minus 15 discontinuous? (5 points)



9.

If f(x) is discontinuous, determine the reason.

f of x equals the quantity x squared plus 4 for x less or equal to 1 and equals x plus 3 for x greater than 1 (5 points)



10.

If f(x) is a continuous function defined for all real numbers, f(-10) = -2, f(-8) = 5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value? (5 points)

1.

Use the graph below to list the x value(s) where the limits as x approaches from the left and right of those integer values(s) are not equal.

A graph is shown beginning at the open point negative two comma negative four continuing to the open point negative one negative one up to a maximum at zero comma zero and back down to the open point one comma negative one. The graph begins again at the closed point one comma two and then condinues down to infinity along the asymptote x equals three then from negative infinity along the asymptote of x equals three the graph increases to the closed point five comma zero. A noncontinuous closed point exists at negative one comma negative two. (10 points)

2.

Find limit as x approaches four of quantity x squared minus sixteen divided by quantity x minus four . You must show your work or explain your work in words. (10 points)


3.

Find limit as x approaches 4 from the left of the quotient of the absolute value of the quantity x minus 4, and the quantity x minus 4 . You must show your work or explain your work in words. (10 points)


4.

A ball’s position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2 + 350.

What is the velocity of the ball after 2 seconds?

Include units in your answer. (10 points)


5.

The cost in dollars of producing x units of a particular telephone is C(x) = x2 – 2500. (10 points)

a. Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 103. Include units in your answer.

b. Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.