InterviewSolution
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InterviewSolution
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Evaluate `lim_(xrarr0)((1-cosxsqrt(cos2x)))/(x^(2)).` |
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Answer» `lim_(xto0)((1-cosxsqrt(coss)))/(x^(2))` `=lim_(xto0){((1-cosxsqrt(cos2x)))/(x^(2))xx((1+cosxsqrt(cos2x)))/((1+cosxsqrt(cos2x)))}` `=lim{((1-cos^(2)xcos2x))/(x^(2))xx(1)/((1+cosxsqrt(cos2x)))}` `=lim_(xto0)((1-cos^(2)xcos2x))/(x^(2))xxlim_(xto0)(1)/((1+cosxsqrt(cos2x)))` `lim_(xto0){(1-cos^(2)x(1-2sin^(2)x))/(x^(2))xx(1)/((1+1sqrt1))` `((1-cos^(2)x+2sin^(2)xcos^(2)x))/(x^(2))xx1/2` `=1/2xxlim_(xto0)((sin^(2)x+2sin^(2)xcos^(2)x))/(x^(2))xx1/2xxlim_(xto0)(sin^(2)(1+2cos^(2)x))/(x^(2))` `=1/2xxlim_(xto0)((sinx)/(x))^(2)xxlim_(xto0)(1+2cos^(2)x)` `1/2xx1^(2)xx(1+2xx1^(2))=3/2.` |
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