evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.)\n…

evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.)\n lim_{t\rightarrow2}\frac{t^{4}-2}{2t^{2}-3t + 1}

evaluate the limit using the appropriate limit law(s). (if an answer does not exist, enter dne.)\n lim_{t\rightarrow2}\frac{t^{4}-2}{2t^{2}-3t + 1}

Answer

Explanation:

Step1: Substitute $t = 2$ into the function

First, substitute $t = 2$ into the numerator $t^{4}-2$ and the denominator $2t^{2}-3t + 1$. For the numerator: $2^{4}-2=16 - 2=14$. For the denominator: $2\times2^{2}-3\times2 + 1=2\times4-6 + 1=8 - 6+1=3$.

Step2: Calculate the limit value

Since substituting $t = 2$ into the rational - function $\frac{t^{4}-2}{2t^{2}-3t + 1}$ gives a well - defined real number, the limit is equal to the value of the function at $t = 2$. The limit $\lim_{t\rightarrow2}\frac{t^{4}-2}{2t^{2}-3t + 1}=\frac{14}{3}$.

Answer:

$\frac{14}{3}$