A problem of finding limit in higher numbers~ Find the limit of LIM x → 1 (1-x) Tan π X / 2?

A problem of finding limit in higher numbers~ Find the limit of LIM x → 1 (1-x) Tan π X / 2?

(1-x)tg(pix/2)
=(1-x)sin(pix/2)/cos(pix/2)
Variable substitution y = 1-x
The limit when y tends to zero
ysin(pi(1-y)/2)/cos(pi(1-y)/2)
=ycos(piy/2)/sin(piy/2)
=cos(piy/2)*(piy/2)/sin(piy/2)*(2/pi)
Since SiNx / X tends to 1, when x tends to 0
Then the above formula tends to cos0 * 1 * (2 / PI) = 2 / PI

A problem of limit (Advanced Mathematics)
Find LIM (x - > 0 +) (1 / ln (x + radical (x ^ 2 + 1)) - 1 / ln (x + 1)), give a basic idea and process

The derivative of Ln (x + radical (x ^ 2 + 1)) is 1 / radical (x ^ 2 + 1), so LIM (x - > 0) (LN (x + radical (x ^ 2 + 1))) / X (with lobida) = LIM (x - > 0) 1 / radical (x ^ 2 + 1) = 1 indicates that when X - > 0, ln (x + radical (x ^ 2 + 1)) ~ X. (this is the key) divides the original formula, and the denominator is ln (x + radical (x ^ 2 + 1)) ln (x + 1)

Ask for help! A high number problem about the limit
X = 0 is the ()
A continuous point
B can go to break point
C jump breakpoint
D type II discontinuity
Thank you^
When x tends to 0 - according to the image of inverse scale function, we can see that 1 / X is negative infinity. How can we find the limit of minus 1 to the power of negative infinity of 2

D
f(0-) = 0
F (0 +) is positive infinity