Question

l'hopital's rule to find the limit as x approaches 0 sin 4x/tan 5x

Answer 1

applying the rule

limit as x --> 0 of 4 cos 4x / 5 sec^2 5x

the value of cos 4x and sec^2 5x at x = 0 = 1

therefore required limit is 4/5

Answer 2

thank you

Answer 3

how about this one?
lim x-> -infinity x^2e^x

Answer 4

as x-> - infinity for e^x this approaches 0 ( 1 / e^(infinity))

Answer 5

so this equals x^2 * 0 = 0

limit is 0