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 – 3x2 + 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