Among (i) `underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underset(xtooo)limsec^(-1)((sinx)/(x)).`

Among (i) lim_(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim_(xtooo) sec^(-1)((sinx)/(x)).

Find the limits: (a) underset(x to 0)lim (1-cos x)/(x^2) (b) underset(x to 0)lim (tanx-sinx)/(x^(3)) (c ) underset(x to 1)lim ""(cos (pix//2))/(1-x)

Find (i) underset(x to 5)(lim 6) (ii) underset(x to 2)(lim x) (iii) underset(x to 3)(lim [x + 2]) (iv) underset(x to 2)(lim 4x + 2])

Evaluate lim_(xtooo) x^((1)/(x)).

Differentiate each of the following w.r.t. x: (i) tan^(-1)((1-cosx)/(sinx))" "(ii)tan^(-1)((cos x -sinx)/(cosx +sinx))

tan^(-1)((cosx+sinx)/(cos x-sinx))

Evaluate lim_(xtooo) 2^(x-1)tan((a)/(2^(x))).

(i)intsec^(7) x. sin x dx" "(ii) int(1)/(sinx. cos^(2) x)dx