Answer to Question #233586 in Calculus for Mis

Question #233586
find the limit at infinity of (2+x)30 x (4+x)5 / (2-x)35
1
Expert's answer
2021-09-06T14:27:14-0400
limx(2+x)30×(4+x)5(2x)35\lim\limits_{x\to\infin}\dfrac{(2+x)^{30}\times(4+x)^5}{(2-x)^{35}}

=limx(2x+xx)30×(4x+xx)5(2xxx)35=\lim\limits_{x\to\infin}\dfrac{(\dfrac{2}{x}+\dfrac{x}{x})^{30}\times(\dfrac{4}{x}+\dfrac{x}{x})^5}{(\dfrac{2}{x}-\dfrac{x}{x})^{35}}

=limx(2x+1)30×(4x+1)5(2x1)35=\lim\limits_{x\to\infin}\dfrac{(\dfrac{2}{x}+1)^{30}\times(\dfrac{4}{x}+1)^5}{(\dfrac{2}{x}-1)^{35}}

=(0+1)30×(0+1)5(01)35=\dfrac{(0+1)^{30}\times(0+1)^5}{(0-1)^{35}}

=1=-1


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