Calculus Examples

Determine if Continuous f(x)=1/(x^2)
Step 1
Find the domain to determine if the expression is continuous.
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Step 1.1
Set the denominator in equal to to find where the expression is undefined.
Step 1.2
Solve for .
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Step 1.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.2
Simplify .
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Step 1.2.2.1
Rewrite as .
Step 1.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 1.2.2.3
Plus or minus is .
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
Since the domain is not all real numbers, is not continuous over all real numbers.
Not continuous
Step 3