# Thread: Find the limits of the following in all steps:

1. ## Find the limits of the following in all steps:

Hey i am not really good with limits that have sin,cos, and etc so i was wondering if i could have some help with these 2 questions in finding the limits.

A) lim[sin(1-√x )] / (x-1)
x>>1

B) lim cos(π/ √19-3 sec 2t )
t>>0

2. Hi

Im not sure what you mean on the second one.

First one:

$\displaystyle\lim_{x\to1} \frac{sin(1-\sqrt{x})}{x-1}=\displaystyle\lim_{x\to1}-\frac{sin(1-\sqrt{x})}{(1-\sqrt{x})(1+\sqrt{x})} =-\frac{1}{2}$

I used the fact that $(1-x)=(1-\sqrt{x})(1+\sqrt{x})$ on the denominator to be able to use the standard limit.

3. Originally Posted by Twig
Hi

Im not sure what you mean on the second one.

First one:

$\displaystyle\lim_{x\to1} \frac{sin(1-\sqrt{x})}{x-1}=\displaystyle\lim_{x\to1}-\frac{sin(1-\sqrt{x})}{(1-\sqrt{x})(1+\sqrt{x})} =-\frac{1}{2}$

I used the fact that $(1-x)=(1-\sqrt{x})(1+\sqrt{x})$ on the denominator to be able to use the standard limit.
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Oh thankyou so much, thats the same answer i got for the first one but i thought i did it wrong cuz i did it with cosine, but thanks still that helped alot