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

On which of the following intervals is the function f given by f(x) = x^(100) + sin x –1 decreasing ?

Find the range of each of the following functions. (i) f(x)=2-3x, x in R, x gt 0 (ii) f(x)=x^(2)+2x, x is a real number. (iii) f(x) = x, x is a real number

Prove that the function f(x)= x^(2) is continuous at x=0.

Discuss the continuity of the following functions: f(x)= sin x. cos x

Discuss the continuity of the following functions: f(x)= sin x - cos x

Find the zero of the polynomial in each of the following cases. (i) f (x) = x +2 (ii) f (x) = x-2 (iii) f (x) =2x +3 (iv) f (x) =2x -3 (v) f (x) =x ^(2) (vi) f (x) = px, p ne 0 (vii) f (x) = px + q,p ne 0 pq are real numbers.