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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
`because" "cos|x|" is differentiable everywhere as "cos(-x)=cosx`
Also using wavy curve method
`(x^(2)-1)|x^(2)-3x+2|={{:((x-1)^(2)(x+1)(x+2)),(AAx in (-00","-1)uu(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`
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