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Calculus Examples
limx→∞arctan(−ex)
Step 1
Step 1.1
Consider the limit with the constant multiple −1 removed.
limx→∞ex
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 limx→∞−ex=−∞.
limt→−∞arctan(t)
Step 3
The limit as t approaches −∞ is −π2.
−π2