Limits
the limit as x approaches -5 of
(2x+10)/(x2+2x-15)
-1/4
Find the derivative of:
f(x)= pi^2 +e^3 -4
0
Find the second derivative of (x+3)/(x-1)
8/(x-1)^3
The definition of a derivative in limit notation
What is the limit as x ->a of (f(x)-f(a))/(x-a)
or
the limit as h->0 of (f(x+h)-f(x))/h
If y=(x3+1)2, then dy/dx=
6x2(x3+1)
If x2+xy-y=2, find dy/dx
(-2x-y)/(x-1)
or
(2x+y)/(1-x)
True/False: If f(a) is undefined, then the limit as x approaches a will also be undefined.
False: Not Necessarily
If f(x)=cos(3x), then f'(pi/3)=
0
If the graph of f'''(x) of some function f is a line of slope 2, then f'(x) could be what type of function?
A cubic function
If the limit as x approaches infinity of
6x2/(200-kx-kx2) = 2/3, then k=
-9
If f(9)=3 and f'(9)=-2, find the derivative of x2f(x2) at x=3
-90
If f(x)=sin2(3-x) then f'(0)=? Your answer can be left in terms of sin and cos.
-2sin3cos3