Without L'Hôpital

Calculus Level 2

Find the value of the limit without using L'hôpital's rule lim ⁡ x → ∞ cos ⁡ ( x 2 x ) \displaystyle \lim_{x\to \infty}\cos\left(\frac{x}{2^x}\right)


The answer is 1.

Hjalmar Orellana Soto by Hjalmar Orellana Soto , 24, Chile

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Roberto Gallotta
Dec 29, 2015

We know 2^x has an exponential growth, which means, when X->infinite, 2^x grows to infinite quicker than x; so the fraction would be some number divided by infinite, which we know gives us 0 as a result. cos(0) is 1, which is the solution to the problem; all done without using the L'hôpital's rule.

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Joshua Vacaro
Jan 1, 2016

As you can see 2^x increases tremendously than x coz it is exponential. That's why we will get inf/inf but the infinity in the denominator is much larger so this will give approximately 0. And cos(0)=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...