Calculus Examples

$lim_{t \to a} \frac{s (a) - s t}{5 - t}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $t$ approaches $a$ .

$\frac{lim_{t \to a} s (a) - s t}{lim_{t \to a} 5 - t}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $a$ .

$\frac{lim_{t \to a} s (a) - lim_{t \to a} s t}{lim_{t \to a} 5 - t}$

Step 3

Evaluate the limit of $s (a)$ which is constant as $t$ approaches $a$ .

$\frac{s (a) - lim_{t \to a} s t}{lim_{t \to a} 5 - t}$

Step 4

Move the term $s$ outside of the limit because it is constant with respect to $t$ .

$\frac{s (a) - s lim_{t \to a} t}{lim_{t \to a} 5 - t}$

Step 5

Split the limit using the Sum of Limits Rule on the limit as $t$ approaches $a$ .

$\frac{s (a) - s lim_{t \to a} t}{lim_{t \to a} 5 - lim_{t \to a} t}$

Step 6

Evaluate the limit of $5$ which is constant as $t$ approaches $a$ .

$\frac{s (a) - s lim_{t \to a} t}{5 - lim_{t \to a} t}$

Step 7

Evaluate the limits by plugging in $a$ for all occurrences of $t$ .

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Step 7.1

Evaluate the limit of $t$ by plugging in $a$ for $t$ .

$\frac{s (a) - s a}{5 - lim_{t \to a} t}$

Step 7.2

Evaluate the limit of $t$ by plugging in $a$ for $t$ .

$\frac{s (a) - s a}{5 - a}$