Calculus Examples

Evaluate Using the Squeeze Theorem limit as x approaches infinity of arctan(-e^x)
limxarctan(ex)
Step 1
Since the function ex approaches , the negative constant 1 times the function approaches .
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Step 1.1
Consider the limit with the constant multiple 1 removed.
limxex
Step 1.2
Since the exponent x approaches , the quantity ex approaches .
Step 1.3
Since the function ex approaches , the negative constant 1 times the function approaches .
Step 2
Substitute t for ex and let t approach since limxex=.
limtarctan(t)
Step 3
The limit as t approaches is π2.
π2
 x2  12  π  xdx