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
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
Hi
Im not sure what you mean on the second one.
First one:
$\displaystyle \displaystyle\lim_{x\to1} \frac{sin(1-\sqrt{x})}{x-1}=\displaystyle\lim_{x\to1}-\frac{sin(1-\sqrt{x})}{(1-\sqrt{x})(1+\sqrt{x})} =-\frac{1}{2}$
I used the fact that $\displaystyle (1-x)=(1-\sqrt{x})(1+\sqrt{x}) $ on the denominator to be able to use the standard limit.