Question

If 0 < a < b,then $\underset{n\to \infty }{lim}(b^n+a^n{)}^{1/n}$ is equal to

• A. e
• B. a
• C. b
• D. 1

Answer 1

The correct option is C

b

$\underset{n\to \infty }{lim}b{(1+{\left(\frac{a}{b}\right)}^n)}^{1/n}$

We can see that the expression which is multiplies with "b" becomes $\underset{x\to 0}{lim}b{(1+x)}^x$
Which we know is equal to 1.
= $b.1$

=$b$