Calculus Examples

Evaluate the Limit limit as x approaches 2 of cos((pix)/3)
Step 1
Evaluate the limit.
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Step 1.1
Move the limit inside the trig function because cosine 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
Combine and .
Step 3.2
Move to the left of .
Step 3.3
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 3.4
The exact value of is .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: