Question

plseeeee solve this

Answer 1

@amistre64

Answer 2

what is the limit as x approaches 1 of the top part of ot?

Answer 3

*it

Answer 4

looks Lhopital to me

Answer 5

or by squeeze thrm, either way ...

if i plug into my calculator very small values for x, they converge to 0 i believe

Answer 6

please can u solve it

Answer 7

.... i did

Answer 8

mighta made a mistake tho

Answer 9

but i m not getting an answer
answer is -2/pi

Answer 10

.... yeah, i loathe limits in trig

Answer 11

\[\frac{tan(x\frac{pi}{2})}{\frac{1}{x-1}}\]
\[\frac{\frac{pi}{2}sec^2(x\frac{pi}{2})}{-\frac{1}{(x-1)^2}}\]thats not it
\[\frac{{x-1}}{cot(x\frac{pi}{2})}\]
\[\frac{1}{-\frac{pi}{2}csc^2(x\frac{pi}{2})}\]
hmmm

Answer 12

that should do it ....

Answer 13

\[\lim_{x \rightarrow 1} (x - 1)\tan(x\frac{\pi}{2})\]
\[\Large \lim_{x \rightarrow 1} \frac{(x - 1)sin\frac{x\pi}{2}}{\cos\frac{x\pi}{2}}\]
L'ho
\[\Large \lim_{x \rightarrow 1} \frac{\sin\frac{x\pi}{2}-\frac{\pi}{2}(x - 1)\cos\frac{x\pi}{2}}{-\frac{\pi}{2}\sin \frac{x\pi}{2}}\]

That's how I would do it

Answer 14

Or, even simpler:
\[\lim_{x \rightarrow 1} (x - 1)\tan({x\pi \over 2})\]
\[\Large \lim_{x \rightarrow 1} \frac{x - 1}{\cos\frac{x\pi}{2}}\lim_{x \rightarrow 1}\sin\frac{x\pi}{2}\]
\[\Large \lim_{x \rightarrow 1} \frac{x - 1}{\cos \frac{x\pi}{2}}\]
Now this is of the form 0/0 so we apply L'hos
\[\Large \lim_{x \rightarrow 1} \frac{1}{-\frac{\pi}{2}\sin\frac{x\pi}{2}}=\frac{1}{-\frac{\pi}{2}}=-\frac{2}{\pi}\]

Answer 15

@Meepi
thank u