Question

Questions about Limits, please HELP someone.

Answer 1

\[\lim_{x \rightarrow 0} x / 2 (1-\sqrt{x+1)}\]

Answer 2

Clarify the question please. Is it
\[(x/2)(1-\sqrt{x+1)}\]

or
\[x/(2(1-\sqrt{x+1})\]

Answer 3

the second one. im not sure of how to do the fraction over thingy hee

Answer 4

Ans is ±1

Answer 5

Solution

Applying L'hopital rule:

Differentiating both numerator and denominator:

\[\lim_{x \rightarrow 0} 1/2(0-1/2\sqrt{x+1})\]

simplifying this we get,
\[\lim_{x \rightarrow 0}-\sqrt{x+1}\]

Now substitue 0 instead of x, you will get your answer

Answer 6

okay thank you. can i know, is there any way we can do by using the conjugate method?

Answer 7

sure

Posting now

Answer 8

\[\lim_{x \rightarrow 0} x/2(1-\sqrt{x+1}) * (1+\sqrt{x+1})/(1+\sqrt{x+1})\]

\[\lim_{x \rightarrow 0} x*(1+\sqrt{x+1})/2(1-x-1)\]

\[\lim_{x \rightarrow 0} 1+\sqrt{x+1}/2\]

Now Substitute x=0 and get your answer :)

Answer 9

In The last step I forgot the brackets.

\[\lim_{x \rightarrow 0} (1+\sqrt{x+1})/2\]

Should make it more clear now

Answer 10

okay thank you so much :)