lim x- -24

sqrt(x^2+49) - 25 / x+24

The answer in the book is -48/50 which we get by multiplying the top and bottom by the conjugate and eliminating a x+24 term BUT why doesn't L'Hospital's rule work here? Isn't it 0/0?

Question

lim x-> -24

sqrt(x^2+49) - 25 / x+24

The answer in the book is -48/50 which we get by multiplying the top and bottom by the conjugate and eliminating a x+24 term BUT why doesn't L'Hospital's rule work here? Isn't it 0/0?

raden · Answer

yeah, it would be 0/0 u can use L'hop

anonymous · Answer

but you get a different answer if you do

anonymous · Answer

if you take the derivative of the top, its 1/sqrt(x^2+49) and the bottom is just 1 which comes out to 1/25

raden · Answer

u are wrong
hint : derivative of sqrt(f(x)) is f'/2*f(x)
so, what's derivative of sqrt(x^2+49) - 25 ?

anonymous · Answer

yeah you are right, I messed up the derivative. thanks for your response anyway.

raden · Answer

damn.. typo 
derivative of sqrt(f(x)) is f'/2*sqrt(f(x))