How do you find the limit of this?

[cgug123]

Hi!
First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was unable to see how to go from there. Attempted l'hospital's way and was once again confounded by how to proceed. Would appreciate hints.

 

[Mark44]

Hi!
First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was unable to see how to go from there. Attempted l'hospital's way and was once again confounded by how to proceed. Would appreciate hints.

There's a special limit that you need to know to be able to do problems like this: $\lim_{x \to 0}\frac{\sin(x)} x = 1$. You also need to know some of the properties of limits, such as $\lim_{x \to a} f(x) - g(x) = \lim_{x \to a} f(x) - \lim_{x \to a} g(x)$, provided that all of the limits actually exist.

The limit of your problem can be split into two limits, and some algebra manipulation can be performed to get into the form I mentioned first.

Be advised that this is a homework or coursework-type problem, so should be posted in the Homework & Coursework sections, not here in the technical math sections.