January 14th, 2018, 01:31 PM  #1 
Newbie Joined: Jan 2018 From: MI Posts: 11 Thanks: 1  Calc Limits
Please help with limits. Also, I would like to have an explanation so I can understand how to do this. Image: https://ibb.co/ne2i6m I understand limits in general, just not what this problem asks for; help is very appreciated, please, and thank you! Last edited by skipjack; January 15th, 2018 at 12:48 AM. 
January 14th, 2018, 02:16 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,195 Thanks: 1152 
$\lim \limits_{x\to 2+} f(x)$ means the limit of $f(x)$ as $x$ approaches $2$ from the right. Similarly $\lim \limits_{x\to 2} f(x)$ refers to when $x$ approaches $2$ from the left. So for example $\lim \limits_{x\to 2+} f(x) = \lim \limits_{x\to 2}~ 6x^2 + 2m = 24+2m$ I leave you to complete the problem 
January 14th, 2018, 02:19 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,508 Thanks: 2513 Math Focus: Mainly analysis and algebra 
The first asks for the limit as $x$ approaches $2$ from above (the rightsided limit). The second asks for the limit as $x$ approaches $2$ from below (the leftsided limit). The rest should be selfexplanatory. 
January 14th, 2018, 06:38 PM  #4 
Newbie Joined: Jan 2018 From: MI Posts: 11 Thanks: 1 
Thank you both for your help! I realized that I was not putting my answer in terms of m which resulted in my confusion.

January 14th, 2018, 09:53 PM  #5 
Newbie Joined: Jan 2018 From: somewhere Posts: 14 Thanks: 2 Math Focus: Algebraic Number Theory / Differential Fork Theory  Indeed, m is an independent variable and not an input to the function so it has to be considered when finding the values. Were you able to solve the third part?

January 15th, 2018, 08:05 AM  #6 
Newbie Joined: Jan 2018 From: MI Posts: 11 Thanks: 1  

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