Best solutions to - "Evaluate the following limits. a) limx→∞7+9x211+7x b) limx→−∞7+9x211+7x"

Emeli Hagan

Answered question

2021-10-28

Evaluate the following limits.
a)

lim_{x \to \infty} \frac{\sqrt{7 + 9 x^{2}}}{11 + 7 x}

lim_{x \to - \infty} \frac{\sqrt{7 + 9 x^{2}}}{11 + 7 x}

gwibdaithq

Skilled2021-10-29Added 84 answers

lim_{x \to \infty} \frac{\sqrt{7 + 9 x^{2}}}{11 + 7 x}

taking

x^{2}

common from numerator

lim_{x \to \infty} \frac{x \sqrt{\frac{7}{x^{2}} + 9}}{11 + 7 x}

taking x common from denominator

lim_{x \to \infty} \frac{x (\sqrt{\frac{7}{x^{2}} + 9})}{x (\frac{11}{x} + 7)}

= lim_{x \to \infty} \frac{\sqrt{\frac{7}{x^{2}} + 9}}{\frac{11}{x} + 7}

x \to \infty, \frac{1}{x^{2}} \to 0

and

\frac{1}{x} \to 0

= \frac{7}{x^{2}} \to 0

and

\frac{11}{x} \to 0

So answer is

\frac{\sqrt{0 + 9}}{0 + 7} = \frac{3}{7}

lim_{x \to - \infty} \frac{\sqrt{7 + 9 x^{2}}}{11 + 7 x} = lim_{x \to - \infty} \frac{x \sqrt{\frac{7}{x^{2}} + 9}}{x (\frac{11}{x} + 7)}

lim_{x \to - \infty} \frac{\sqrt{\frac{7}{x^{2}} + 9}}{((\frac{11}{x} + 7)}}

x \to - \infty, \frac{1}{x^{2}} \to 0 \Rightarrow \frac{7}{x^{2}} \to 0

x \to - \infty; \frac{1}{x} \to 0 \Rightarrow \frac{11}{x} \to 0

= \frac{\sqrt{0 + 9}}{0 + 7} = \frac{3}{7}

2021-12-05

x^(1/(1-x)

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