Calculus Polynomials, Equations And Interval Exercise Help

1) Find the limit:

lim_x–>-1 (2x³-2x²+x+3)

2) Find the limit:
lim_x–>1 [(x-1)(x+2)/(x-1)]

3) What is the coordinate of the center of this circle:
(x -1)² + (y +3)² = 4

4) What is the radius of this circle:
(x -1)² + (y +3)² = 4

5) let f(x)= 2x-1 , g(x)= 3x² + 4, find this composition:
f(x) o g(x) =?

6) Find derivative of f(x):
f(x)= x

7) find derivative of g(x).
g(x)= 7x

8) find derivative of f(x).
f(x)= 3x²-5x +1

9) Find slope of tanget line to y = 2x²-3 at x = -1

10) Find derivartive of y = 1/x

11) find derivative of y = square root of x

12) Use implicit derivative to fine y’ for the expression given below:
yx – x = x²

13) Find derivative of y = 2^x

14) find derivative of y = 5^2x-3

15) Find derivative of f(x) = ln (3x²-x)

16) find derivative of the g(x) = log₂ x

17) Let f(x)=x² -6x +2
Find coordinate of the minimum point, using derivative.

18) Find increasing interval for f(x) = x²-4x +3

19) Find decreasing interval for f(x) = x²-4x +3

20) Find derivative of y = x. lnx
hint: use product rule