Evaluate `lim_(xto0) (x(e^(x)-1))/(1-cosx)` is equal to
Evaluate `lim_(xto0) (x(e^(x)-1))/(1-cosx)` is equal to
A. `e`
B. `(1)/(e)`
C. 1
D. none of these
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Correct Answer - D
`underset(xto0)lim(x(e^(x)-1))/(1-cosx)=underset(xto0)lim(2x(e^(x)-1))/(4"sin"^(2)(x)/(2))`
`=2underset(xto0)lim[((x//2)^(3))/("sin"^(2)(x)/(2))]((e^(x)-1)/(x))=2`
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