# Question on limits and integration

by aditya bhatt   Last Updated October 20, 2019 05:20 AM - source

Let $$f$$ be a continuous function on $$[0,1]$$. Then the $$\lim_{n\to ∞}\int_{0}^{1}nx^nf(x)$$ is equal to ?

What I did: I tried for $$f(x)=x$$ and on computing the integral and the limit I got the answer = $$1 \implies f(1)$$[ according to the options]. However, I do not know if this is a valid way to generalize the answer for all functions continuous on $$[0,1]$$.