Calculus Examples

$\frac{lim_{x \to 0.25 π} 1 - \tan (x)}{\sin (x) - \cos (x)}$

Step 1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0.25 π$ .

$\frac{lim_{x \to 0.25 π} 1 - lim_{x \to 0.25 π} \tan (x)}{\sin (x) - \cos (x)}$

Step 2

Evaluate the limit of $1$ which is constant as $x$ approaches $0.25 π$ .

$\frac{1 - lim_{x \to 0.25 π} \tan (x)}{\sin (x) - \cos (x)}$

Step 3

Move the limit inside the trig function because tangent is continuous.

$\frac{1 - \tan (lim_{x \to 0.25 π} x)}{\sin (x) - \cos (x)}$

Step 4

Evaluate the limits by plugging in $0.25 π$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $0.25 π$ for $x$ .

$\frac{1 - \tan (0.25 π)}{\sin (x) - \cos (x)}$

Step 4.2

Multiply $0.25$ by $π$ .

$\frac{1 - \tan (0.78539816)}{\sin (x) - \cos (x)}$