Question

Can someone help me with the problem?
f(x)={ln 2x, 0<x<2
{2lnx, x >or= 2
The limit lim x-> 2 f(x) is?

Answer 1

is it 2ln 2?

Answer 2

f(x) => ln 4 when x is "barely less than" 2 and then becomes 2 ln2 at x = 2 These two numbers are equal. The funtion has a slope discontinuity at x=2 but remains continuous there.

The limit is 2ln2 = ln4 = 1.3863..

Answer 3

o alright thank you drwls

Answer 4

By definition of Limit :
The left limit value should be equal to right limit value .
lim f(x) = lim f(x) = lim f(x)
x->a- x->a+ x->a
In our problem say
The left limit values lies between 0 to 2
lim ln 2x = lim 2 ln x
x->2- x->2+
==> ln 4 = 2 ln 2
[Hint ln a ^b = b ln a ]
[ln 4 = ln 2^2 = 2 ln 2 ]
==> ln 4 = ln 4
So the left limit should be equal to right limit.
So limit exist at x = 2
Thanks !
Bye !
More information contact my mail.

Bye for now !