Help me how to find the limit of this operation
- Thread starter Haseo0
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pka
Elite Member
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- Jan 29, 2005
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Your handwritting is very hard to deal with.
As I read the limit it is \(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + x\cos (x)} - \sqrt {1 + x} }}{{{x^2}}}\)
Multiply numerator & denominator by \({\sqrt {1 + x\cos (x)} + \sqrt {1 + x} }\)
Rearrange as \(\left( {\dfrac{1}{{\sqrt {1 + x\cos (x)} + \sqrt {1 + x} }}} \right)\left( {\dfrac{{\cos (x) - 1}}{x}} \right)\)
As I read the limit it is \(\mathop {\lim }\limits_{x \to 0} \frac{{\sqrt {1 + x\cos (x)} - \sqrt {1 + x} }}{{{x^2}}}\)
Multiply numerator & denominator by \({\sqrt {1 + x\cos (x)} + \sqrt {1 + x} }\)
Rearrange as \(\left( {\dfrac{1}{{\sqrt {1 + x\cos (x)} + \sqrt {1 + x} }}} \right)\left( {\dfrac{{\cos (x) - 1}}{x}} \right)\)
Steven G
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- Dec 30, 2014
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You say that you tried L'Hopital's rule. That is great but if you do not show us your work then it is hard to help you. pka gave you one way of solving the limit but you wanted to do it a different way. So please show us your work so we can see what is going on.