Calculus Examples

Evaluate the Limit ( limit as x approaches 4 of |x-4|)/(x-4)
Step 1
Evaluate the limit.
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Step 1.1
Move the limit inside the absolute value signs.
Step 1.2
Split the limit using the Sum of Limits Rule on the limit as approaches .
Step 1.3
Evaluate the limit of which is constant as approaches .
Step 2
Evaluate the limit of by plugging in for .
Step 3
Simplify the answer.
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Step 3.1
Simplify the numerator.
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Step 3.1.1
Multiply by .
Step 3.1.2
Subtract from .
Step 3.1.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 3.2
Divide by .