1) a) lim1

() =

b) lim1+

() =

c) lim0

() =

d) lim1

() =

e) lim1+

() =

f) lim2

() =

g) lim2+

() =

2) Find the following limits;

a) lim1

+||

= b) lim

2

|24|

2= c) lim

1

|23+2|

1=

3) Explain why a) lim0+

1

= and b) lim

1

= 0 with graph.

4) if : {0} , Calculate, lim0+

1

1+2 2

5) Calculate the following limits;

a) lim

2+4

92+2= b) lim

0

2

3=

PART2

1) For the function f (x)= 2x2 + x - 2 , which of the following is a simplified algebraic expression in terms of a and h to find the slope of

the secant between (a, f (a)) and (a+h, f (a+h)) ?

a. 4a + 2h + 1 b. 4a + 2h - 1 c. 2a + 4h + 1 d. 2a - 4h + 1

2) For the function f (x) = 2x2 + x - 2 , find the equation of the tangent to the curve when x = -1

a. y = -3x + 1 b. y = -3x - 4 c. y = 3x + 2 d. y = 3x 4

3) Differentiate the function f (x) = 4x2 - 3x - 1 .

4) Find the slope of the tangent to the function y = 6x2 - (4/x) when x = 2.

a. 25 b. 24 c. 21 d. 12

5) The position of a particle can be modelled by the function x (t) = 4t3 - 2t2 + 6t - 1 where t = time in seconds and x is measured in

metres. How fast was the particle moving after 6 seconds?

a. 827 m/s b. 782 m/s c. 699 m/s d. 414 m/s

6) If f '(x) = 4x2 - 5 , which of the following could be f (x) ?

a. 5x3 - 5x b. 2x3 - 2x c. 4x3 - 5x d. (4/3)x3 - 5x + 3

7) Given the graph of f '(x) shown below: Which of the following could be the graph of f (x)? Choose one answer.

8) Consider the slopes of the tangent lines to the given curve, shown above, at each of the five points shown. List these five slopes in decreasing order.

9) Find the slope of the tangent line to the graph of each function at the given point. (you may use the space provided below)

10) Find the derivative of each function.

a) b)

c) d)

11) If the tangent to the graph of f(x) = x2 2ax + 3 at x = 1 is parallel to the line 2x y = 1, find a.

12) Find the derivative of each function with respect to the variable given at each option.

13) Given that f(1) = 2, f (1) = 1, g(1) = 2 and g(1) = 3, find the value of h(1) in each of the following cases.

14) Find the derivative of each function.

a)

b)

c)

d)

e)

Success

15) Suppose that f and g are two functions such that f(5) = 1, f (5) = 6, g(5) = 3 and g(5) = 2. Find each value.

16) Find the derivative of the following expressions.

17) Find the second derivative ( f (x) ) of each function. Hint: f (x) = (f (x) )

18) Find the third derivative ( f (x) ) of each function. Hint: f (x) =( (f (x) ))