If `f(x)={sin^(-1)(sinx),xgt0`
`(pi)/(2),x=0,then
cos^(-1)(cosx),xlt0`

Iff(x)={sin^(-1)(sinx),x >0, pi/2,x=0,tcos^(-1)(cosx),x<0

If f(x)={{:(sin(cos^(-1)x)+cos(sin^(-1)x)",",xle0),(sin(cos^(-1)x)-cos(sin^(-1)x)",",xgt0):} then at x = 0

Differentiate the following function with respect to x : sin^(-1)(sinx),x in [0,2pi] cos^(-1)(cosx),x in [0,2pi] tan^(-1)(tanx),x in [0,pi]-{pi/2}

If f(x)={{:((sin(a+1)x+2sinx)/x", "xlt0),(2" ,"x=0),((sqrt(1+bx)-1)/x" ,"xgt0):} is continuous at x = 0, then find the values of 'a' and 'b'.

Show that cot^(-1)x={(tan^(-1)(1//x),xgt0),(pi+tan^(-1)(1//x),xlt0):}

Show that cot^(-1)x={(tan^(-1)(1//x),xgt0),(pi+tan^(-1)(1//x),xlt0):}

Show that the function f(x) defined by : f(x)={{:((sinx)/x+cosx", "xgt0),(2", "x=0),((4(1-sqrt(1-x)))/x", "xlt0):} is continuous at x = 0.

if f(x)={{:((sin(p+1)x+sinx)/(x),xlt0),(x,x=0),((sqrt(x^(2)+x)-sqrt(x))/(x^(3//2)),xgt0):} is continuous at x=0 then (p,q) is

Let f(x){:{(1+sinx", "xlt0),(x^(2)-x+1ge0):} Then

Let f(x){:{(1+sinx", "xlt0),(x^(2)-x+1ge0):} Then