Math 150 Exam 2

1.. Sketch the graph of an example of a function f that satisfies all of the given conditions.

lim f(x) = 2, lim f(x) = 0, lim f(x) = 3,

x->0- x->0+ x->4-

lim f(x) = 0, f(0) = 2, f(4) = 1

x->4+

Evaluate the limit, if it exists.

2. lim (x3 – 3×2 + 9x)

x->3

3. lim __6x – 9___

x ->0 x3 – 12x + 3

4. lim t3 + 8

t -> -2 t + 2

5. lim x2 – 4x + 4

x -> 2 x2 + x – 6

6. lim (2 + h)3 – 8

h ->0 h

______

7. lim ?(x2 + 9) – 5

x ->4 x + 4

__1___ _1_

8. lim (x + h)2 – x2

h ->0 h

_____

9. lim ?x2 + 1

x -> +?

10. lim x2 – 4x + 4

x -> -? x2 + x – 6

11. Find values of x, if any, at which f is not continuous.

f(x) = x + 2

x2 – 4

If there is x at which f is not continuous, is it a removable discontinuity? Just answer Yes or No. No need to prove it.

12. Use either one of the following formulas to find the derivative of the function. (Not both).

f ?(a) = lim f(x) – f(a)

x -> a x – a

or

f ?(a) = lim f(a + h) – f(a)

h -> 0 h

(a) f(x) = 1 / x

_

(b) f(x) = ?x