Hi. Evaluate. $\displaystyle \lim_{\ x\to 0}\frac{(\arctan{\sqrt{x}})(sinx)-x{\sqrt{x}}}{xe^{\sqrt{x}}-cos{\sqrt{x}}+1}$
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Originally Posted by Shock Hi. Evaluate. $\displaystyle \lim_{\ x\to 0}\frac{(\arctan{\sqrt{x}})(sinx)-x{\sqrt{x}}}{xe^{\sqrt{x}}-cos{\sqrt{x}}+1}$ why makes you think this limit involves Taylor series? looks more like an application of L'Hopital's rule ... maybe more than once.
Originally Posted by skeeter why makes you think this limit involves Taylor series? looks more like an application of L'Hopital's rule ... maybe more than once. The prof said we have to solve it with taylor series.
Either way I would substitute $\displaystyle u=\sqrt{x}$ before doing anything. And notice that the limit really should only be from the right.
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