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STATEMENT -1 : f(x)= (1 -cos(1-cosx))/x...

STATEMENT -1 : `f(x)= (1 -cos(1-cosx))/x^(4)` is continuous if f(0) , 1/8
and
STATEMENT -2 : ` lim_( x to 0^(+)) f(x) = lim_(x to 0^(+)) f(x) = 1/8`

A

Statement -1 is True, Statement -2 is True, Statement -2 is a correct explantion for Statement -1

B

Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -1

C

Statement -1 is True , Statement -2 is Flase

D

Statement -1 is Flase , Statement - 2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • If f(x) = x sin (1//x), x ne 0 , then lim_(x to 0) f(x) =

    A
    1
    B
    0
    C
    `-1`
    D
    not exist

  • If f(x) is continuous and f(9/2)=2/9 , then : lim_(x to 0) f((1-cos 3x)/(x^2)) =

    A
    `2/9`
    B
    `9/2`
    C
    18
    D
    81

  • Let f:R to ((-1)/2 , 1/2) be an odd function such that lim_( xto0) f(x) exists. Then, lim_( x to 0) 1/(2f(x)-1) equals

    A
    0
    B
    `1/2`
    C
    2
    D
    `-1`