Draw the graph of the function
`f(x)={("1 if "xgt0),("0 if "x=0),("-1 if "xlt0):},x inR`

The range of the function : f(x)=2-3x,x inR,xgt0 is

Show that the Signum function f:R->R , given by f(x)={(1,xgt0),(0,x=0),(-1,xlt0)) is neither one-one nor onto

Using Rolle's theorem show that derivative of the function f(x) ={underset(0 " ""for"" "x=0)(x ins .(pi)/(x) " ""for"" "xgt0) . Vanishes at an infinite set of points of the interval (0.1)

Prove that the function If f(x)={:{((x)/(1+e^(1//x)) ", " x ne 0),(" "0", " x=0):} is not differentiable

Consider f,g and h be three real valued functions defined on R. Let f(x)={:{(-1", "xlt0),(0", "x=0"),(1", "xgto):} "g(x)(1-x^(2))andh(x) "be such that" h''(x)=6x-4. Also, h(x) has local minimum value 5 at x=1 The area bounded by y=h(x),y=g(f(x))between x=0 and x=2 equals

Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is differentiable at x=0 and f'(0)=0

Prove that the function f(x)= {:{((sinx)/x , xlt 0), (x^(2)+1, x ge 0):} in x in RR is continuous

Draw a graph of the function f(x) = cos^(-1) (4x^(3)-3x), x in [-1,1] and find the ara enclosed between the graph of the function and the x-axis varies from 0 to 1.

The function f is defined as : f(x)={{:(1","x gt0),(0"," x =0),(-1","x lt 0):} The range of f is :

If f:RtoR defined by f(x)={(4x-1" for " xgt4),(x^(2)-2" for "-2lexlt4),(3x+4" for "xlt-2):} find f(5)+f(0)+f(-5)