Below is the graph of fx for each of the given points

Question

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

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

3. Evaluate ,If it exists.

4. For evaluate the indicated limits, if they exist

5. For answer each of the following questions.

a. Evaluate 

b. Evaluate 

c. Write down the equation(s) of any horizontal asymptotes for the function.

6. Find the derivative of the following functions

7. Find the tangent line to 

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:

B. Integration by trignometric substitution:

11. Find the inverse function of :

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.