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lim(x->pi/4)(cot^3x-tanx)/cos(x+pi/4) is...

`lim_(x->pi/4)(cot^3x-tanx)/cos(x+pi/4)` is equal to (A) `8` (B) `4sqrt(2)` (C) `8sqrt(2)` (D) `2sqrt(2)`

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Knowledge Check

  • lim_(xto pi/4) (cot^3x-tanx)/(cos(x+pi/4)) is

    A
    4
    B
    `8sqrt2`
    C
    8
    D
    `4sqrt2`

  • lim_(x to pi//4) (sqrt(2)cos x-1)/(cot x-1) equals

    A
    `1/sqrt(2)`
    B
    `1/2`
    C
    `1/(2sqrt(2))`
    D
    1

  • If cosxdy/dx-y sin x=6x, (0ltxltx/2)and y(pi/3)=0 , then y(pi/6) is equal to (a) pi^(2) /(2sqrt 3) (b) -pi^(2) /(2sqrt 3) (c) -pi^(2) /(4sqrt 3) (d) (c) -pi^(2) /2

    A
    (a) `pi^(2) /(2sqrt 3)`
    B
    (b) `-pi^(2) /(2sqrt 3)`
    C
    (c) `-pi^(2) /(4sqrt 3)`
    D
    (d) (c) `-pi^(2) /2`

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    The numerical value of tan((pi)/(3))+2tan((2 pi)/(3))+4tan((4 pi)/(3))+8tan((8 pi)/(3)) is equal to (A)-5sqrt(3)(B)-(5)/(sqrt(3))(C)5sqrt(3)(D)(5)/(sqrt(3))

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    lim_(x rarr pi/4)(sqrt(cos x)-sqrt(sin x))/(x-(pi)/(4))

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