Calculus Examples

Evaluate the Limit ( limit as x approaches 0 of sin(5x))/(3x)
Step 1
Evaluate the limit.
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Step 1.1
Move the limit inside the trig function because sine is continuous.
Step 1.2
Move the term outside of the limit because it is constant with respect to .
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
The exact value of is .
Step 3.2
Cancel the common factor of and .
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Step 3.2.1
Factor out of .
Step 3.2.2
Cancel the common factors.
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Step 3.2.2.1
Factor out of .
Step 3.2.2.2
Cancel the common factor.
Step 3.2.2.3
Rewrite the expression.
Step 3.3
Divide by .