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Question

Find the limits of the following expression $$\displaystyle\frac{(3-x)(x+5)(2-7x)}{(7x-1)(x+1)^3}$$, $$(1)$$ when $$x=\infty$$, $$(2)$$ when $$x=0$$.


Solution

(1) When $$x\to\infty$$
Dividing numerator and denominator of the given exprssion with $$x^4$$, We get:
$$\displaystyle\lim_{x\to \infty}\dfrac{1/x(3/x-1)(1+5/x)(2/x-7)}{(7-1/x)(1+1/x)}\\= \dfrac{0\times-1\times1\times-7}{7\times1}=0$$

(2) When $$x=0$$ expression will become
$$\dfrac{3\times5\times2}{-1\times1}=-30$$


Mathematics

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