Homework Statement
find the integral from (2 to infinity) of 1/(1+e^x)
Homework Equations
The Attempt at a Solution
lim(t-->infinity) integral from (2 to t) of 1/(1+e^x)
1/1+e^x = (1+e^x-e^x)/(1+e^x)
= 1-e^x(1+e6x)
when you solve the integral:
x-ln(1+e^x) between 2 and t...
Homework Statement
evaluate lim(x->0) (tan^8(t))dt(between 0 and sin^2x)
Homework Equations
The Attempt at a Solution
[tan^8(sin^2(x))]/sin^18(x)
my book says to use l'hospital's rule, so i continued with
[8tan^7(sin^2x)*sec^2(sin^2(X))*2sinxcosx]
but my book says i should...
Homework Statement
let f(x)=(4t^3+4t)dt(between 2 and x)
if g(x) = f^(-1)(x), then g'(0)=?
Homework Equations
The Attempt at a Solution
f'(x) = 4x^3+4x
annd i already don't know where to go from here.. help?
Homework Statement
solve the integral [abs(x+1)(3+abs(x))]/(x+1) between -3 and 1
Homework Equations
The Attempt at a Solution
when x<-1 then [abs(x+1)(3+abs(x))]/(x+1) = [-(x+1)(3-x)]/(x+1) = -(3-x)
when -1<x<0 then [abs(x+1)(3+abs(x))]/(x+1) = (x+1)(3-x)/(x+1) = 3-x
when x>0...
by this same logic, shouldn't i have
if x>2, abs(abs(x-2)-abs(x)) = -(abs(x-2-x)) = -(2)
since abs(x-2) and abs(x) are positive but abs(abs(x-2)-abs(x)) is negative?
i know it should be a positive 2 since that gets me to the right answer... but i don't see why?