Question

find the limit at infinity of (2+x)30 x (4+x)5 / (2-x)35

Answer 1

$$\lim\limits_{x\to\infin}\dfrac{(2+x)^{30}\times(4+x)^5}{(2-x)^{35}}$$

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

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

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

$$=-1$$