If `f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)++(x^2)/((1+x^2)^n)+ ,` then at `x=0,f(x)` has no limit (b) is discontinuous is continuous but not differentiable (d) is differentiable

If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)+ , then at x=0,f(x) (a)has no limit (b) is discontinuous (c)is continuous but not differentiable (d) is differentiable

If f(x)=(x)/(1+x)+(x)/((x+1)(2x+1))+(x)/((2x+1)(3x+1))+…"to "infty ,then at x = 0,f(x) (a) has no limit (b) is discontinuous (c) is continuous but not differentiable (d) is differentiable

If f(x)=sum_(n=0)^oo x^n/(n!)(loga)^n , then at x = 0, f(x) (a) has no limit (b) is discontinuous (c) is continuous but not differentiable (d) is differentiable

Discuss the continuity and differentiability of f(x)={1-x ,x 2

If f(x)={[1/(x^2)-1/(x^2),xlt0],[sin^(-1)(x+b),x gt-0]} then at x=0,f(x) is (a)continuous if b=0 (b)discontinuous for any real b (c)differentiable for b=+-1 (d)non-differentiable for any real b

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

If f(x)={(1-cos x)/(x sin x),x!=0 and (1)/(2),x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (continuous but not differentiable (d)neither continuous nor differentiable

If f(x) = (x^(2)-x)/(x^(2)+2x) , then d/dx [f^(-1)(x)] =

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable

If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)continuous and differentiable (b)differentiable but not continuous (c)continuous but not differentiable (d)neither continuous nor differentiable