Question
Use a graphing calculator to graph the function. (a) Determine the limit from the graph. (b) Explain how your answer could be determined from the expression for $f(x).$$$\lim _{x \rightarrow-\infty} \frac{\sqrt{36 x^{2}+2 x+7}}{3 x}$$
Step 1
We do this by dividing each term in the numerator and the denominator by the highest degree term in the denominator, which is $x^2$. This gives us: $$\lim _{x \rightarrow-\infty} \frac{\sqrt{36+\frac{2}{x}+\frac{7}{x^2}}}{3}$$ Show more…
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Use a graphing calculator to graph the function. (a) Determine the limit from the graph. (b) Explain how your answer could be determined from the expression for $f(x) .$ $$ \lim _{x \rightarrow \infty} \frac{\sqrt{36 x^{2}+2 x+7}}{3 x} $$
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Use a graphing calculator to graph the function. (a) Determine the limit from the graph. (b) Explain how your answer could be determined from the expression for $f(x).$ $$\lim _{x \rightarrow \infty} \frac{\sqrt{9 x^{2}+5}}{2 x}$$
Use a graphing calculator to graph the function. (a) Determine the limit from the graph. (b) Explain how your answer could be determined from the expression for $f(x) .$ $$ \lim _{x \rightarrow \infty} \frac{\sqrt{9 x^{2}+5}}{2 x} $$
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