# Limits of function

• Mar 10th 2007, 08:10 PM
Sasuke12
Limits of function
Please give me some tips on how to solve this..

f: (1,∞) -> IR

f(x) = (1/6)((√x)-1)------(√7x) +√7--- (x/6)(√(x-1))
-------------------- + ------------- + -------------
-------√(x²-1) 3 ----------√(x+3)--------√(x²-1)

find exact value of

lim f(x)
x->1+

Thanks.
• Mar 11th 2007, 12:15 AM
CaptainBlack
Quote:

Originally Posted by Sasuke12
Please give me some tips on how to solve this..

f: (1,∞) -> IR

f(x) = (1/6)((√x)-1)------(√7x) +√7--- (x/6)(√(x-1))
-------------------- + ------------- + -------------
-------√(x²-1) 3 ----------√(x+3)--------√(x²-1)

find exact value of

lim f(x)
x->1+

Thanks.

Consider the terms separately. Look at the last one:

(x/6) sqrt(x-1) / sqrt(x^2 - 1)

divide top and bottom by x:

(x/6) sqrt(x-1) / sqrt(x^2 - 1) = (1/6) sqrt(x-1) / sqrt(1 - 1/x^2)

Now as x -> inft the denominator goes to 1, and the numerator goes to infty.
Therefore the limit of this term is +infty.

The other terms are all positive for large x, so it does not matter how they
behave for large x we still have:

lim(x->infty) f(x) = infty

RonL