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underset(xrarr0)"lim"(cos x)/(pi-x)...

`underset(xrarr0)"lim"(cos x)/(pi-x)`

Text Solution

Verified by Experts

The correct Answer is:
`1/pi`
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Knowledge Check

  • Consider the following statements: I. underset(xrarr0)lim (x^(2))/(x) exists. II. ((x^(2))/(x)) is not continuous at x = 0. III. underset(xrarr0)(lim)(|x|)/(x) does not exist Which of the above statements are correct?

    A
    A) I, II, and III
    B
    B) I and II
    C
    C) II and III
    D
    D) I and III
  • underset(xrarr0)("lim")("sin"(pi"cos"^(2)x))/(x^(2)) is equal to

    A
    `pi/(2)`
    B
    1
    C
    `-pi`
    D
    `pi`
  • lim_(xrarr0)""(sin|x|)/(x)

    A
    is equal to1
    B
    is equal to 0
    C
    is equal to infinity
    D
    does not exist
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    Consider the function: f(x)={{:((alphacosx)/(pi-2x),"if "xne(pi)/(2)),(3,"if "x=(pi)/(2)):} Which is continuous at x=(pi)/(2) , where alpha is a constant. What is underset(xrarr0)(lim)f(x) equal to?

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