Question

Can someone please help me solve this problem
THANK

Answer 1

`lim_(x \rightarrow 0) (xcsc(2x))/(cos(5x)) = (0)/(0) \\\therefore\\lim_(x \rightarrow 0) (xcsc(2x))/(cos(5x)) = lim_(x \rightarrow 0) (x)/(sin(2x)cos(5x))\\= lim_(x \rightarrow 0) (1)/(2cos(2x)cos(5x) -5sin(2x)sin(5x)) = (1)/(2)`