hi i'm tryng to solve this limit but i get an indeterminate form( (e)^sinx) limit of x-> infinite of ((sqrt(x)+2^x+2)/(sqrt(x)+2^x))^(sqrtx*sinx) any idea how to solve this?
+118628 hi i'm tryng to solve this limit but i get an indeterminate form( (e)^sinx) limit of x-> infinite of ((sqrt(x)+2^x+2)/(sqrt(x)+2^x))^(sqrtx*sinx) any idea how to solve this?
\(\displaystyle\lim_{x\rightarrow\infty}\;\left[\frac{\sqrt{x}+2^x+2}{\sqrt{x}+2^x}\right]^{(\sqrt{x}*sinx)}\)
This is probably wrong, I am not very good at these but I will give it a shot.
\(=\displaystyle\lim_{x\rightarrow\infty}\;\left[\frac{\sqrt{x}+2^x}{\sqrt{x}+2^x} +\frac{2}{\sqrt{x}+2^x}\right]^{(\sqrt{x}*sinx)}\\ =\displaystyle\lim_{x\rightarrow\infty}\;\left[1+\frac{2}{\sqrt{x}+2^x}\right]^{(\sqrt{x}*sinx)}\\~\\ =\displaystyle\lim_{x\rightarrow\infty}\;\left[1+\frac{\frac{2}{\sqrt{x}}}{1+\frac{2^x}{\sqrt{x}}}\right]^{(\sqrt{x}*sinx)}\\ ~\\=\displaystyle\lim_{x\rightarrow\infty}\;\left[1+0\right]^{(\sqrt{x}*sinx)}\\ ~\\=1 \)
Yes, it's probably wrong.
