if `f(x)=sum_(k=0->n) a_k |x|^k` ,where `a_i's` are real constants then `f(x)` is `(A)` continuous at `x= 0` for all `a_i (B)` differentiable at `x= 0` for all `a_i (C)` differentiable at `x= 0` for all `a_(2k +1)` (D) none of these

If f(x) = sum_(r=1)^(n)a_(r)|x|^(r) , where a_(i) s are real constants, then f(x) is a. continuous at x = 0, for all a_(i) b. differentiable at x = 0, for all a_(i) in R c. differentiable at x = 0, for all a_(2k+1) = 0 d. None of the above

If f(x)=sum_(n=0)a_(n)|x|^(n), where a_(i) are real constants,then f(x) is

If f(x)=sum_(n=0)a_(n)|x|^(n), where a_(i) are real constants,then f(x) is

If f(x)=sum_(k=0)^(n)a_(k)|x-1|^(k), where a_(i)in R, then

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then A. f(x) is continuous for all x in [0, 2) B. f(x) is differentiable for all x in [0, 2) - {1} C. f(X) is differentiable for all x in [0, 2)-{(1)/(2),1} D. None of these

Let f(x)=a+b|x|+c|x|^4 , where a , ba n dc are real constants. Then, f(x) is differentiable at x=0, if a=0 (b) b=0 (c) c=0 (d) none of these

Let f(x)=a+b|x|+c|x|^(4), where a,b and c are real constants.Then,f(x) is differentiable at x=0, if a=0 (b) b=0( c) c=0(d) none of these

If f(x)=|ln|x|, then (a)f(x) is continuous and differentiable for all x in its domain (b) f(x) is continuous for all for all x in its domain but not differentiable at x=+-1 (c) f(x) is neither continuous nor differentiable at x=+-1 (d) none of these

Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. Then, f(x) is differentiable at x=0 , if a=0 (b) b=0 (c) c=0 (d) none of these