Calculus Practice Test 1

Show all work and justify each step.

(1) Find the difference quotient for at

    (a)

    (b)

    (c)

    (d)

    (e)

(2) Find an equation of the line tangent to at the point

    (a)

    (b)

    (c)

    (d)

    (e)

(3) If then find

    (a) does not exist

    (b) 2

    (c) 1

    (d) 0

    (e)

(4) If find

    (a)

    (b)

    (c)

    (d)

    (e)

(5) Which of the following functions is continuous at the point but not differentiable at

    (a)

    (b)

    (c)

    (d)

    (e) no such function exists

(6) Find if

    (a)

    (b)

    (c) 0

    (d) not enough information given

    (e) does not exist

(7) Determine so that the following function is continuous. Choose an interval that contains

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    (a)

    (b)

    (c)

    (d)

    (e)

(8) Suppose Compute

    (a) 1

    (b)

    (c) 0

    (d)

    (e)

(9) If and are differentiable functions such that and find

    (a) 0

    (b) 5

    (c) 4

    (d)

    (e) not enough information given

(10) If and are differentiable functions such that and find

    (a)

    (b)

    (c)

    (d) 0

    (e) not enough information

(11) Find

    (a)

    (b)

    (c)

    (d) does not exist

    (e) 0

(12) If that is

    (a) 9

    (b) 2

    (c) 106

    (d) 25

    (e) 0

(13) Solve for

    (a) 4

    (b)

    (c) no solutions

    (d)

    (e)

(14) If and are continuous functions with and

find

    (a) 0

    (b) 6

    (c) 3

    (d) 5

    (e) not enough information given

(15) Find an equation of the normal line to the graph of at

    (a)

    (b)

    (c)

    (d)

    (e)

(16) Find the point(s) on the graph of where the tangent line to the graph of is parallel to the line

(17) Use the definition of the derivative to show that when

(18) Use the quotient rule to determine the derivative of

(19) Find an equation for the tangent line to the graph of at the endpoint wish -coordinate 1.

(20) Evaluate without using a calculator or L'Hospitals's rule.