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The value of `lim_(xrarr0)(e^(x)-cos2x-x)/(x^2)` , is

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The value of `lim_(xrarr0)(e^(x)-cos2x-x)/(x^2)` , is
A. 2
B. `(1)/(2)`
C. `(3)/(2)`
D. `(5)/(2)`
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Correct Answer - D
`lim_(xto0)(e^(x)-cos2x-x)/(x^2)`
`lim_(xto0)((e^(x)-1-x)(1-cos2x-))/(x^2)`
`lim_(xto0) (((x^2)/(2!)+(x^3)/(3!)+....)+2sin^2x)/(x^2)`
` =lim_(xto0) {((1)/(2!)+(x)/(3!)+.....)+2((sinx)/(x))^2}=(1)/(2!)+2xx1^2=(5)/(2)`
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