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If lim(xto0) [1+xln(1+b^(2))]^(1//x)=2bs...

If `lim_(xto0) [1+xln(1+b^(2))]^(1//x)=2bsin^(2)theta,bgt0," and "thetain(-pi,pi],` then the value of `theta` is

Text Solution

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The correct Answer is:
D
`e^(ln(1+b^(2)))=2bsin^(2)theta`
or `" "sin^(2)theta=(1+b^(2))/(2b)=1" as "(1+b^(2))/(2b)ge1`
`theta=+-pi//2`
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Knowledge Check

  • lim_(xto0)xsin(1/x) is

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

  • lim_(xto0)"sin"(1)/(x) is

    A
    0
    B
    1
    C
    `oo`
    D
    Doest not exist

  • lim_(xto0)(sqrt(1+x^(2))-1)/(1-cosx)=

    A
    1
    B
    `1/2`
    C
    `1/4`
    D
    `oo`

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