Calculus Examples

Evaluate the Limit limit as x approaches pi of xsec(x)
Step 1
Split the limit using the Product of Limits Rule on the limit as approaches .
Step 2
Move the limit inside the trig function because secant is continuous.
Step 3
Evaluate the limits by plugging in for all occurrences of .
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Step 3.1
Evaluate the limit of by plugging in for .
Step 3.2
Evaluate the limit of by plugging in for .
Step 4
Simplify the answer.
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Step 4.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because secant is negative in the second quadrant.
Step 4.2
The exact value of is .
Step 4.3
Multiply by .
Step 4.4
Move to the left of .
Step 4.5
Rewrite as .
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: