find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise…

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise exist, enter dne.)\n lim_{t \to -infty} \frac{2 t^{2}+t}{t^{3}-7 t+1} \nresources\nread it

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise exist, enter dne.)\n lim_{t \to -infty} \frac{2 t^{2}+t}{t^{3}-7 t+1} \nresources\nread it

Answer

Explanation:

Step1: Divide numerator and denominator by (t^{3})

$$\lim_{t\rightarrow-\infty}\frac{2t^{2}+t}{t^{3}-7t + 1}=\lim_{t\rightarrow-\infty}\frac{\frac{2t^{2}}{t^{3}}+\frac{t}{t^{3}}}{\frac{t^{3}}{t^{3}}-\frac{7t}{t^{3}}+\frac{1}{t^{3}}}$$ Simplify the fractions: $$=\lim_{t\rightarrow-\infty}\frac{\frac{2}{t}+\frac{1}{t^{2}}}{1-\frac{7}{t^{2}}+\frac{1}{t^{3}}}$$

Step2: Evaluate the limit

As (t\rightarrow-\infty), (\frac{2}{t}\rightarrow0), (\frac{1}{t^{2}}\rightarrow0), (\frac{7}{t^{2}}\rightarrow0) and (\frac{1}{t^{3}}\rightarrow0) $$\lim_{t\rightarrow-\infty}\frac{\frac{2}{t}+\frac{1}{t^{2}}}{1-\frac{7}{t^{2}}+\frac{1}{t^{3}}}=\frac{0 + 0}{1-0 + 0}$$

Answer:

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