SOLUTION: Use lim(x goes to 0) sinx/x = 1 to evaluate lim(x goes to 0) 1-cosx/x^2. I know the answer should be 1/2 but am not sure how to get that answer. Thanks!
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Question 770584: Use lim(x goes to 0) sinx/x = 1 to evaluate lim(x goes to 0) 1-cosx/x^2. I know the answer should be 1/2 but am not sure how to get that answer. Thanks!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Are you allowed to use l'Hôpital's Rule?
If so, take the derivatives of the numerator and denominator: \right)\ =\ \sin(x)\ \ \ )
and }{dx}\ =\ 2x)
.
Then take the limit }{2x}\ =\ \large\lim_{x\right{0}}\,\LARGE\frac{1}{2}\ \cdot\ \large \lim_{x\right{0}}\,\LARGE\frac{\sin(x)}{x}\ =\ \frac{1}{2})
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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