I have the problem ((square root of h^2+4h+5)-(square root of 5))/h. I am supposed to be finding the limit as h approaches 0 from the right. We are supposed to solve it algebraically and I believe I should be using a the conjugate but I am not exactly sure how to set it up, any help would be appreciated. Thanks
Yes, use the conjugate.
Multiply top and bottom by (√(h^2+4h+5) + √5)/(√(h^2+4h+5) + √5) , which has a value of 1,
to let
limit (√(h^2+4h+5) - √5)/h * (√(h^2+4h+5) + √5)/(√(h^2+4h+5) + √5) as h --> 0
= lim ( h^2 + 4h + 5 - 5)/(h(√(h^2+4h+5) + √5))
= lim h(h + 4)/(h(√(h^2+4h+5) + √5))
= lim (h + 4)/(√(h^2+4h+5) + √5) as h ---> 0
= 4/(2√5)
= 2√5/5 after rationalizing