Extend the definition of the following by continuity `f(x)=(1-cos7(x-pi))/(5(x-pi)^2)` at the point `x=pi` .

Find the domain of definition the following function: f(x)=log_(10)(1-log_7(x^2-5x+13))+cos^(-1)(3/(2+sin\ (9pi)/2))

Evaluate the following limit: (lim)_(x->pi)(sqrt(5+cos x)-2)/((pi-x)^2)

Discuss the continuity of the function f(x) ={:{((1+cos x)/(tan^2 x) ", "x ne pi),((1)/(2) ", " x=pi):}, at x=pi .

Evaluate the definite integral int_(pi/2)^(pi) e^x[(1-sin x)/(1-cos x)] dx

Find the values of k so that the function f is continuous at the indicated point in f(x)={{:((kcosx)/(pi-2x), ifx!=pi/2 ),(3, ifx=pi/2):} at x=pi/2

Examination the function f(x) given by f(x)={((cosx)/(pi/2-x) ,, x != pi/2),(1 ,, x = pi/2):} ; for continuity at x=pi/2

Evaluate the following limit: (lim)_(x->pi/2)((pi/2-x)sin x-2cos x)/((pi/2-x)+cot x)

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

Find the value of k so that the function f defined by f(x)={(kcosx)/(pi-2x), "if"\ \ x\ !=pi/2" 3,if"\ x=pi/2 is continuous at x=pi/2

let f(x)=e^(cos^(-1)sin(x + pi/3)) then f((8pi)/9) and f((-7pi)/4)