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Topic: how to find limit lim (sqrt(x+1) - sqrt(x)
Replies: 6   Last Post: Jun 20, 2012 2:44 AM

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 Angela Richardson Posts: 42 From: UK Registered: 6/22/11
Re: how to find limit lim (sqrt(x+1) - sqrt(x)
Posted: Apr 10, 2012 1:35 AM
 att1.html (1.2 K)

Let x=tan^2(y)
sqrt(x+1)-sqrt(x)=sqrt(1+tan^2(y))-tan(y)=sec(y)-tan(y)=(1-sin(y))/cos(y)
as y-->pi/2   x-->infinity
d/dy 1-sin(y) = -cos(y)
d/dy cos(y) = -sin(y)
cos(y)/sin(y) = 0 when y=pi/2 so x-->0

________________________________
From: calc999 <discussions@mathforum.org>
To: discretemath@mathforum.org
Sent: Monday, 9 April 2012, 22:51
Subject: how to find limit lim (sqrt(x+1) - sqrt(x)

I am having hard time understanding how to find the limit for when x goes to infinity for lim (sqrt(x+1) - sqrt(x). Can you help me understand the steps?

Date Subject Author
4/9/12 calc999
4/9/12 Ben Brink
4/10/12 calc999
4/10/12 Ben Brink
4/10/12 Angela Richardson
6/20/12 Cool Jessica
6/20/12 Ben Brink