Question

Why is the limit of (1-cos(x+5))/(x+5) as x approaches -5 equal to zero?

Answer 1

are you familiar with l'hopital's rule?

Answer 2

not yet, I only know that there is a theorem that says that the limit of 1-cosx/x as x approaches 0 is zero. Is that related to this?

Answer 3

yes it is related. just let y=x+5 and you have lim y->0 (1-cosy)/y

so back to your theorem this is equal to 0

Answer 4

l'hopital's rule says if you separately differentiate the top and bottom of the original expression and then take the limit, then the final expression is equal to this.

Answer 5

but the limit is as x->-5

Answer 6

If y = x+5 then lim y->0 of y = lim x ->-5 of x+5

Answer 7

okay , got it thanks :)