In which of the following cases, the function f(x) has vertical tangent at x = 0 ?
(ii) `f(x)=sgnx`

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? f(x)=x^(2//3)

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? (v) f(x)={{:(0","," if "xlt0),(1","," if "xge0):}

The function f(x)=x^(x) has

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

Consider the following statements: I. The function f(x)=|x| is not differentiable at x = 1 II. The function f(x)=e^(x) is differentiable at x = 0 Which of the above statements is/are correct?

Which of the following function is not differentiable at x=0?f(x)=min{x,sin x}f(x)={[0,x>=0x^(2),x<0( c) f(x)=x^(2)sgn(x)

For which of the following functions f(0) exists such that f(x) is continuous at x=0f(x)=(1)/((log_(e)|x|) b.f(x)=(cos((sin|x|)/(x))) c.f(x)=x sin((pi)/(x)) d.f(x)=(1)/(1+2^( cot x))

Which of the following functions is/are discontinuous at x=0?f(x)=sin((pi)/(2x)),x!=0 and f(x)=1

Draw the graph of each of the following constant functions: (i) f(x)=2 for all x""inR (ii) f(x)=0 for all x""inR (iii)f(x)=-2 for all x""inR