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Lt x−2 2 x+2 - 16 4 x -16 pls evaluate the limit tommorow is my exam

Lt x−2
 
2x+2-16
4x-16 
pls evaluate the limit tommorow is my exam
 

Grade:12th Pass

4 Answers

Arun
25750 Points
6 years ago
Dear Ashwin
 
this is 0/0 form.
now you can put L’hospital rule here.
lt(x--->2)  2x+2 * ln2 / 4x ln4
lt(x--->2)  2x+2 * ln2 / 4x * 2 *ln2
lt(x--->2)  2x * 22/2* 4x   
now put limit
4 *4 / 2 * 16
 = ½
 
Regards
Arun (askIITians forum expert)
 
ASh
62 Points
6 years ago
what is L hospital rule,
 
aditya verma
47 Points
6 years ago
L hospital rule is a rule for solving limit of the 0/0 forms... its derivation can be done by ab initio method also...
Aditya Gupta
2081 Points
5 years ago
simply factorise (2^(x+2) – 16)/(4^x – 16) as 4(2^x – 4)/[(2^x – 4)(2^x+4)]=4/(2^x+4)
now put x=2
we get 4/(2^2+4)= 4/8
=1/2

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