Question

Determine the limit using l'hopital's rule of lim h->0 1/h, arctanx/x dx

Answer 1

you should write this equation with buttom "Equation"

Answer 2

\[\lim h \rightarrow0, 1/h \int\limits_{0}^{h} (arctanx/x) dx\]

Answer 3

this integral is dificult for me but if you want to know the solve http://www.wolframalpha.com/

Answer 4

I don't think we need the integral
we should be able to use the fundamental theorem of calculus here

Answer 5

\[\frac d{dh}\int_{0}^{h}\frac{\tan^{-1}x}x dx=\frac{\tan^{-1}h}h\]

Answer 6

the answe is 1?

Answer 7

Therefor\[\lim_{h \rightarrow 0}\frac{\int_{0}^{h}\frac{\tan^{-1}x} xdx}h=\lim_{h \rightarrow 0}\frac{\tan^{-1}h}h=\lim_{h \rightarrow 0}\frac1{1+h^2}=1\]yep, that's what I got :)

Answer 8

oh there is 0/0 indefinite

Answer 9

i miss that

Answer 10

it says to use l'hospital anyway

Answer 11

Is that using l'hopitals rule ?

Answer 12

yep

Answer 13

Perfect thanks so much!