We meet again.
I'm just going to review the easy stuff that I keep forgetting to look over!
I. L'Hopital's Rule:
lim f(x)/f(x)=0
x-->0
*When this occurs it means to take the derivative of top and bottom then plug in for the limit. f^1(x)/g^(x)
EXAMPLE:
lim 3(x-4)/x^2-14 =0/0
x-->4
3/2x = 3/2(4)=3/8
II. Derivatives of Integrals:
EXAMPLE:
F(x)= integral from 0 to x^2 sin(t)
sin(x^2)(2x) *the 2x is the derivative of the bounds
III. Definition of Derivative:
*take derivative and plug in number
EXAMPLE:
lim sin(pi+g)-sin(pi)/g
g-->0
It is like sinx @ pi, so take deriv which is cos and plug in pi
cos(pi)=-1
IV. ln integration of a fraction:
EXAMPLES:
*What I put in parenthesis should be absolute value!
integral of 2x+6/x^2+6x
= ln (x^2+6x) +C
integral of cos(x)/sin(x)
= ln (sinx) +C
V. NEED HELP:
Although this only involves taking a derivative, can someone help me on
If f(x)=sin^2x, find f^111(x)
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to find f^111(x) of sin^2(2x) you have to realize that the sin function's derivatives go into a pattern of four.
ReplyDeleteYou simply divide 111 by four finding the remainder of .75 which relates to the third derivative, or -cos(x)
after finding that you multiply the derivative of the inside by the number of times you have to take the derivative which is 111
Your final answer should be -222cos(2x).