Wednesday, May 23, 2018

calculus - Limits problem to find the values of constants - a and b If $lim_{x to infty}(1+frac{a}{x}+frac{b}{x^2})^{2x}=e^2$ Find the value of $a$ and $b$.

Problem :




If $\lim\limits_{x \to \infty}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2x}=e^2$ Find the value of $a$ and $b$.



Please suggest how to proceed this problem :



If we know that $\lim\limits_{x \to \infty}\left( 1+\frac{1}{x}\right)^x= e$



Will this work somehow... please suggest

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