Home
Class 12
MATHS
f(x)=(x^2-1)|x^2-3x+2|+cos|x| is not dif...

`f(x)=(x^2-1)|x^2-3x+2|+cos|x|` is not differentiable at x=a, then `sum_(r=0)^(oo)1/(a^r)` is equal to

A

1

B

2

C

0

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
B
`becausecos|x|` is differentiable everywhere as cos(-x)=cosx
Also using wavy curve method
`(x^(2))|x^(2)-3x+2|={{:((x-a)^(2)(x+1)(x+2)),(AAx in(-oo","-1)cup(2","oo)),(-(x-1)^(2)(x+1)(x-2)),(AAx in(1,2)):}`
`therefore`Not diff. at x=2`therefore`a=2
Now `sum_(r=0)^(oo)(1)/(2^(r))=(1)/(1-(1)/(2))=2`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f (x ) = | 3 - | 2- | x- 1 |||, AA x in R be not differentiable at x _ 1 , x _ 2 , x _ 3, ….x_ n , then sum _ (i= 1 ) ^( n ) x _ i^2 equal to :

If sum_(r=1)^(n)cos^(-1)x_(r)=0, then sum_(r=1)^(n)x_(r) equals to

If f(x)=(4+x)^(n),"n" epsilonN and f^(r)(0) represents the r^(th) derivative of f(x) at x=0 , then the value of sum_(r=0)^(oo)((f^(r)(0)))/(r!) is equal to

Let f:R rarr R^(*) be a derivable function such that f(x+y)=3f(x)f(y),AA x,y in R with f(1)=(2)/(3) ,then sum_(r=1)^(oo)(1)/(f(r)) is equal to

If sum of x terms of a series is S_(x)=(1)/((2x+3)(2x+1)) whose r^(th) term is T_(r) . Then, sum_(r=1)^(n) (1)/(T_(r)) is equal to

If x in R , then f(x)=cos^(-1)((1-x^(2))/(1+x^(2))) is equal to

If x^(2)-x+1=0, then the value of sum_(r=1)^(2010)(x^(r)-(1)/(x^(r)))^(3) is equal to

For x in R ,f(x)=|log2-sinx| and g(x)=f(f(x)) , then (1) g is not differentiable at x=0 (2) g'(0)=cos(log2) (3) g'(0)=-cos(log2) (4) g is differentiable at x=0 and g'(0)=-sin(log2)