Question

Limits,

Can you help me solve this?
http://screencast.com/t/Q45dG1mKKlXT

Just tell me the basic steps that you take to approach a problem like this as clear as you can please, the rest I will understand by my own :/

Answer 1

@ganeshie8 @Hero @skullpatrol @RolyPoly @jhonyy9

Answer 2

Wait a min

Answer 3

Yes off

Answer 4

Ofc**

Answer 5

a and c: Consider one-sided limits
b: Just plug in

Answer 6

\[g(0)\] does not exist
since
\[\lim 0^{-}=-2,\lim 0^{+}=0\]
\[\lim_{t \to 1} t^2=1^2=1\]

Answer 7

AS CLEAR dude or dont post here please!

Answer 8

Hero will help me out thank you all for your efforts though!

Answer 9

\[\lim_{t \to 2^{-}}g(x)=2^2=4\]
\[\lim_{t \to 2^{+}}g(t)=2(2)=4\]
\[\implies \lim_{t \to 4} g(4)=4\]

Answer 10

https://www.desmos.com/calculator/zknxp3usuf

Answer 11

The crux here is, approach a particular point (say t=0 in the first part) and check what values of limit you get...

For t<0,(that means t==>0-) approach g(t) = t-2
and
For t>0 (t==>0+), approach g(t) = t^2

I hope it's clear ... sorry but you can ignore mine though :-( )

Answer 12

thanks salon , and also for 2t how do I approach it? Do I approach it as 0+ or 0- ? As you can see I am a beginner in limits and I need the very very first steps

Answer 13

Look , since the definitions of g(t) given part wise are polynomials, they would be continuous ... so no issue regarding discontinuity... So you need to check only for limit at t=0 only where g(t) changes it's value... Check only in the NEIGHBOURHOOD of t=0 for finding limits...
You have to approach from both sides to check that g(t=>0-) = g(t=>0+) for limit to exist...

Answer 14

ok but what is the use of this part in the problem? http://screencast.com/t/XRYJfhpuS what is it telling me?

Answer 15

Actually this is the one who is telling you everything... These intervals tell you how is g(t) defined...
As per the first one, t<0 means on the left hand side of t=0, the value of g(t)= t-2,
Similarly all these intervals specify how is g(t) defined...
If you plot the graph you would need to know g(t) = t-2 in which interval... and g(t) =t^2 in which interval ... and so on...

Limits physically mean whether you get the same value of function around a point or not...

Answer 16

0 1 and 4