Evaluate the limit using L'Hospital's Rule lim┬(x→∞)⁡〖(7x)^(-1) e^3x 〗

Question

Evaluate the limit using L'Hospital's Rule lim┬(x→∞)⁡〖(7x)^(-1) e^3x 〗

Answer 1

(7x)^(-1)e^3x = e^3x/7x

you need to rewrite the expression as a fraction

take derivatives, separately of numerator and denominator:

3e^3x/7

as x approaches infinity, the expression also approaches infinity, without limit

if you wanted the limit as x approaches zero, then it's 3/7