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For f to be continuous at x = f(0) is gi...

For f to be continuous at x = f(0) is given by
`{:("Column- I " , " Column - II"),("(A)" f(x) = (ln(1 +4x))/x, "(p)" 1/4),("(B)" f(x)=(ln(4+x)-ln4)/x , "(q) 0"),("(C)" f(x) = 1/sinx - 1/tan x , "(r)"4),("(D)" f(x)=(1-cos^(3)x)/( x sin 2x) , "(s)" 3/4):}`

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The correct Answer is:
A, B, C, D
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Knowledge Check

  • If f(x)=(ln(1+x))/x, x in (-1,oo) and f(0)=1 then f(x) is

    A
    decreasing in `(-1,0)` and increasing in `(0,oo)`
    B
    always increasing
    C
    always decreasing
    D
    increasing in `(-1,0)` and decreasing in `(0,oo)`

  • Let f''(x) be continuous at x =0 and f''(0)=4, then "lt"_(x to 0) (sin x -(sin x)^(sin x))/(1- sin x + log sin x) =

    A
    1
    B
    2
    C
    3
    D
    0

  • If f(x) = is continuous at x=0 , where f(x)=((1-cos2x)(3+cos x))/(x tan 4x) , for x!=0 , then f(0)=

    A
    2
    B
    `1/2`
    C
    4
    D
    None of these