22. The function f defined bysin x?a for x=0f(x)= XisTo for x = 01) continuous and derivable at x=02) neither continuous nor derivable at x=03) continuous but not derivable at x=04) continuous but not derivable at x=1

Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = 0

Is the function defined by f(x)={x+5, if x 1 a continuous function?

Let S (x) = int_(x^2) ^(x^3) (lnt) dt (x>0) and H(x) = (S'(x)) / x . Then H(x) is (i) continuous and not derivable in it's domain (ii) continuous and derivable in it's domain (iii) Neither continuous and nor derivable in it's domain (iv) Not continuous and is derivable in it's domain

Is the function defined by f(x)= |x|, a continuous function

is f(x)=|x| a continuous function?

Prove that the function f defined by f(x) = x^3 + x^2 -1 is a continuous function at x= 1.

The function f (x) is continuous at x = 0 of -

Show that the function: f(x) = {:{(2+x,ifxge0),(2-x,ifx<0):} is continuous but not derivable at x=0

If f(x)={(|x+2|)/(tan^(-1)(x+2)), x!=-2 2, x=-2 , then f(x) is continuous at x=-2 (b) not continuous at x=-2 (c) differentiable at x=-2 (d) continuous but not derivative at x=-2