hi everyone :)

how could I solve this :

WITHOUT USING L'HOSPITAL RULE :)

IM LOST :(

When x is very large pi/5^{x} is very small.

When z is very small sin(z) → z, so when x is very large xsin(pi/5^{x}) → x*pi/5^{x}

5^{x} increases much more rapidly than x, so x*pi/5^{x} → 0

Hence, in the limit as x → ∞, xsin(pi/5^{x}) → 0

.