1. Below is the graph of f(x). For each of the given points determine the value of f(a) and lim x→af(x) . If any of the quantities do not exist clearly explain why.
(a) a = -3 (b) a = -1 (c) a = 2 (d) a = 4
![284_Untitled.png](https://secure.tutorsglobe.com/CMSImages/284_Untitled.png)
2. . Below is the graph of f(x). For each of the given points determine the value of f(a) and x→af(x), x→a+f(x) and x→a-f(x)If any of the quantities do not exist clearly explain why.
(a) a = -2 (b) a =1 ( c) a = 3 (d) a = 5
![2327_Untitled.png](https://secure.tutorsglobe.com/CMSImages/2327_Untitled.png)
3. Evaluate
,If it exists.
4. For
evaluate the indicated limits, if they exist
![1305_Untitled.png](https://secure.tutorsglobe.com/CMSImages/1305_Untitled.png)
5. For
answer each of the following questions.
a. Evaluate ![968_Untitled.png](https://secure.tutorsglobe.com/CMSImages/968_Untitled.png)
b. Evaluate ![850_Untitled.png](https://secure.tutorsglobe.com/CMSImages/850_Untitled.png)
c. Write down the equation(s) of any horizontal asymptotes for the function.
6. Find the derivative of the following functions
![1967_Untitled.png](https://secure.tutorsglobe.com/CMSImages/1967_Untitled.png)
![2167_Untitled.png](https://secure.tutorsglobe.com/CMSImages/2167_Untitled.png)
![1303_Untitled.png](https://secure.tutorsglobe.com/CMSImages/1303_Untitled.png)
7. Find the tangent line to ![2242_Untitled.png](https://secure.tutorsglobe.com/CMSImages/2242_Untitled.png)
8. Find the domain of the functions
a. f(x) = 1/ lx2-4l
b. g(x) = 1/ (x2+4x+3)
c. h(x) = √(x2+5x-6)
d. k(x) = 1 / √(x-2)2
e. j(x) = 1 / (x-√(x+2))
f. I(x) = In lx+3l - 5
9. Find the range of the functions
a. f(x) = -x2+6x+5
b. g(x) = lx+3l - 2
c. h(x) = (x-2) / (x+3)
d. k(x) = lx3+4l
e. j(x) = l (x+4) (x-2) l
f. I(x) = l 1/(x-3) l
10. Find the integral of the following
1. Find ∫ x sin(x2) dx.
2. Find ∫ €x cot (€x) dx.
3. Find ∫ sin-1 x dx.
A. Integration by partial fractions:
![2271_Untitled.png](https://secure.tutorsglobe.com/CMSImages/2271_Untitled.png)
B. Integration by trignometric substitution:
![2309_Untitled.png](https://secure.tutorsglobe.com/CMSImages/2309_Untitled.png)
11. Find the inverse function of :
![1506_Untitled.png](https://secure.tutorsglobe.com/CMSImages/1506_Untitled.png)
12 find the inverse of the relation
{(0, –2), (1, 0), (3, 4), (6, 10)}
13. Find the inverse of a given relation and determine whether the inverse is a function.
{(7, 4), (8, 4)}
14. Find the inverse power function.
![314_Untitled.png](https://secure.tutorsglobe.com/CMSImages/314_Untitled.png)