Evaluate the Limit limit as x approaches infinity of 5e^x

Problem

(lim_x→∞)(5)*ex

Solution

1. Identify the behavior of the exponential function ex as the variable x increases without bound.

2. Recall that as x→∞ the value of ex grows infinitely large.

3. Apply the limit property for constants, noting that multiplying a value that approaches infinity by a positive constant results in a value that also approaches infinity.

4. Conclude that the expression increases without bound.

Final Answer

(lim_x→∞)(5)*ex=∞

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