Get the answer to "Evaluate the following limits. a) limx→∞3+8x27+11x b) limx→−∞3+8x27+11x"

Chaya Galloway

Answered question

2021-11-01

Evaluate the following limits.
a)

lim_{x \to \infty} \frac{\sqrt{3 + 8 x^{2}}}{7 + 11 x}

lim_{x \to - \infty} \frac{\sqrt{3 + 8 x^{2}}}{7 + 11 x}

faldduE

Skilled2021-11-02Added 109 answers

The given limits
a)

lim_{x \to \infty} \frac{\sqrt{3 + 8 x^{2}}}{7 + 11 x}

lim_{x \to - \infty} \frac{\sqrt{3 + 8 x^{2}}}{7 + 11 x}

lim_{x \to \infty} \frac{\sqrt{3 + 8 x^{2}}}{7 + 11 x}

= lim_{x \to \infty} \frac{\sqrt{x^{2} (\frac{3}{x^{2}} + 8)}}{x (\frac{7}{x} + 11)}

= lim_{x \to \infty} \frac{x \sqrt{\frac{3}{x^{2}} + 8}}{x (\frac{7}{x} + 11)}

= lim_{x \to \infty} \frac{\sqrt{\frac{3}{x^{2}} + 8}}{\frac{7}{x} + 11}

= \frac{\frac{3}{\infty} + 8}{\frac{7}{\infty} + 112}

= \frac{0 + 8}{0 + 11}

= \frac{8}{11}

b) here

lim \to - \infty

So there will be no effect answer remains

\frac{8}{11}

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