Calculus Examples

Find Where Undefined/Discontinuous f(x)=tan((pix)/2)
Step 1
Set the argument in equal to to find where the expression is undefined.
, for any integer
Step 2
Solve for .
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Step 2.1
Multiply both sides of the equation by .
Step 2.2
Simplify both sides of the equation.
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Step 2.2.1
Simplify the left side.
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Step 2.2.1.1
Simplify .
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Step 2.2.1.1.1
Cancel the common factor of .
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Step 2.2.1.1.1.1
Cancel the common factor.
Step 2.2.1.1.1.2
Rewrite the expression.
Step 2.2.1.1.2
Cancel the common factor of .
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Step 2.2.1.1.2.1
Factor out of .
Step 2.2.1.1.2.2
Cancel the common factor.
Step 2.2.1.1.2.3
Rewrite the expression.
Step 2.2.2
Simplify the right side.
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Step 2.2.2.1
Simplify .
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Step 2.2.2.1.1
Apply the distributive property.
Step 2.2.2.1.2
Cancel the common factor of .
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Step 2.2.2.1.2.1
Cancel the common factor.
Step 2.2.2.1.2.2
Rewrite the expression.
Step 2.2.2.1.3
Cancel the common factor of .
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Step 2.2.2.1.3.1
Cancel the common factor.
Step 2.2.2.1.3.2
Rewrite the expression.
Step 2.2.2.1.4
Cancel the common factor of .
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Step 2.2.2.1.4.1
Factor out of .
Step 2.2.2.1.4.2
Cancel the common factor.
Step 2.2.2.1.4.3
Rewrite the expression.
Step 2.3
Reorder and .
Step 3
The equation is undefined where the denominator equals , the argument of a square root is less than , or the argument of a logarithm is less than or equal to .
, for any integer
Step 4