Calculus Examples

$lim_{x \to 1} \frac{3 - f (x)}{1 - 4 g (x)}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $1$ .

$\frac{lim_{x \to 1} 3 - f (x)}{lim_{x \to 1} 1 - 4 g (x)}$

Step 2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\frac{lim_{x \to 1} 3 - lim_{x \to 1} f (x)}{lim_{x \to 1} 1 - 4 g (x)}$

Step 3

Evaluate the limit of $3$ which is constant as $x$ approaches $1$ .

$\frac{3 - lim_{x \to 1} f (x)}{lim_{x \to 1} 1 - 4 g (x)}$

Step 4

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$\frac{3 - lim_{x \to 1} f (x)}{lim_{x \to 1} 1 - lim_{x \to 1} 4 g (x)}$

Step 5

Evaluate the limit of $1$ which is constant as $x$ approaches $1$ .

$\frac{3 - lim_{x \to 1} f (x)}{1 - lim_{x \to 1} 4 g (x)}$

Step 6

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$\frac{3 - lim_{x \to 1} f (x)}{1 - 4 lim_{x \to 1} g (x)}$

Step 7

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Step 7.1

Evaluate the limit of $f (x)$ by plugging in $1$ for $x$ .

$\frac{3 - f (1)}{1 - 4 lim_{x \to 1} g (x)}$

Step 7.2

Evaluate the limit of $g (x)$ by plugging in $1$ for $x$ .

$\frac{3 - f (1)}{1 - 4 g (1)}$