Question

lim (x tends to pi) (1+sec^3 x)/tan^2 x

Answer 1

x → π 
rewrite tan²x as (sec²x - 1): 

lim (1+ sec³x) / (sec²x - 1) = 
x → π 
now factor the numerator as a sum between cubes 
and the denominator as a difference between squares: 

lim [(1+ secx)(1 - secx + sec²x)] / [(secx + 1)(secx - 1)] = 
x → π 
and now, (1 + secx) canceling out, simplify it as: 

lim (1 - secx + sec²x) / (secx - 1) = 
x → π 

[1 - (-1) + (-1)²] / [(-1) - 1] = 

(1 +1 +1) / (-2) = - 3 /2 

in conclusion: 

lim (1+ sec³x) / tan²x = - 3 /2 
x → π 

I hope it helps 
Bye!

Answer 2

Ans : -3/2

By applying limits when x is not equal to 0.