Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 36

$\displaystyle \lim_{t \to 1} \frac{t^4 + t - 2}{t - 1}$ represents the derivative of some function $f$ at some number $a$. State such an $f$ and $a$ in this case.

Using the slope equation,

$\qquad m = \lim \limits_{x \to a} \displaystyle \frac{f(x) - f(a)}{x - a}$ or $m = \lim \limits_{t \to a} \displaystyle \frac{f(t) - f(a)}{t - a} $

Referring to the formula $f(t) = t^4 + t$ and $a = 1$ by substituting value of $a$ to the function $f(x)$, the result will be the value of $f(a)$ which is $2$

Therefore,

$\qquad f(t) = t^4 + t$ and $a = 1$

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