Illustration: Evaluate Limx→0 1/(si...
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Illustration: Evaluate Limx→0 1/(sin^-1x)^2-1/x^2

JEE/Engineering Exams
Maths
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Illustration: Evaluate Limx→0 1/(sin^-1x)^2-1/x^2
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Limx01(sin-1x)2-1x2 Limx01sin-1x-1x1sin-1x+1x Limx0x-sin-1xxsin-1xx+sin-1xxsin-1x  sin-1x=x+x36+3x540+5x7112+.... x-sin-1x=x-x+x36+3x540+5x7112+....                  =-x316+3x240+5x4112+.... x+sin-1x=x+x+x36+3x540+5x7112+....                   =x2+x26+3x440+5x6112+.... Limx01(sin-1x)2-1x2=Limx0-x316+3x240+5x4112+....x2+x26+3x440+5x6112+....x2x+x36+3x540+5x7112+....2 Limx0-x416+3x240+5x4112+....2+x26+3x440+5x6112+....x41+x26+3x440+5x6112+....2 =-1×26=-13

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