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Find the period of f(x)=sinx+tanx/2+sinx...

Find the period of `f(x)=sinx+tanx/2+sinx/(2^2)+t a n x/(2^3)++sinx/(2^(n-1))+tanx/(2^n)`

Answer

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Knowledge Check

  • lim_(xrarr pi/2) ((1-tanx//2)(1-sinx))/((1-tanx//2)(pi-2x)^3)

    A
    `oo`
    B
    `(1)/(8)`
    C
    `0`
    D
    `(1)/(32)`
  • The period of f(x)=(1)/(2){(| sinx|)/(cos x)+(|cos|)/(sinx)} , is

    A
    `2pi`
    B
    `pi`
    C
    `(pi)/(2)`
    D
    `(pi)/(4)`
  • The largest possible value of the expression f_(n) = sinx_(1) cosx_(2) + sinx_(2)cosx_(3) + .. +sinx_(n)cosx_(1) is where x_(1), x_(2) ...x_(n) are arbitrary real numbers.

    A
    n
    B
    `n/2`
    C
    `n/4`
    D
    `sqrt(n^(2)-1)`
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    lim_(x rarr pi/2) tanx log_e sinx=

    if f(x)=x+sinx , then find (2)/(pi^(2)).int_(pi)^(2pi)(f^(-1)(x)+sinx)dx

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