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InterviewSolution
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`lim_(xrarr(pi)/(2)) ((1-sinx)(8x^(3)-pi^(3)))/(pi-2x)^(4)`A. `-(pi^(2))/(16)`B. `(3pi^(2))/(16)`C. `(pi^(2))/(16)`D. `-(3pi^(2))/(16)` |
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Answer» Correct Answer - D `underset(xrarr(pi)/(2))(lim)((1-sinx)(8x^(3)-pi^(3))cosx)/(pi-2x)^(4)` `=underset(xrarr(pi)/(2))(lim)((1-cos((pi)/(2)-x))(2x-pi)(4x^(2)+pi^(2)+2pix)sin((pi)/(2)-x))/(16((pi)/(2)-x)^(4))` `underset(hrarr0)(lim)((1-cos h)(-2h)sin h)/(16h^(2))underset(xrarr(pi)/(2))(lim)(4x^(2)+pi^(2)+2pix)` `=underset(hrarr0)(lim)((1-cos h)(-2h sin h))/(16h^(4))underset(xrarr(pi)/(2))(lim)(4x^(2)+pi^(2)+2pix)` `=-underset(hrarr0)(lim)((1-cos h))/(8h^(4))(4((pi)/(2))^(2)+pi^(2)+2pi((pi)/(2)))` `=-(3pi^(2))underset(hrarr0)(lim)(2sin^(2).(h)/(2))/(32(h^(2))/(4))` `=-(3pi^(2))/(16)` |
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