Saturday, January 16, 2016

calculus - Evaluate limxtoinftycos(sqrtx+1)cos(sqrtx)


Evaluate lim



For this question I have tried using the squeeze theorem and some trigonometric manipulations such as using 2\sin A\sin B=\cos (A-B) -\cos (A+B). But they were of no use. I also tried using the substitutions like x=1/y Hence as x\to \infty , y\to 0 but still no success.



I could've also tried using L'Hospital rule but I am not able to convert the function in appropriate indeterminate form. Any help would be greatly appreciated

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