Evaluate the Limit limit as x approaches 0 of e^x

Problem

(lim_x→0)(ex)

Solution

1. Identify the type of function. The function ƒ(x)=ex is an exponential function, which is continuous for all real numbers.

2. Apply the property of limits for continuous functions. Since the function is continuous at x=0 the limit can be found by direct substitution.

3. Substitute the value x=0 into the expression.

e0

4. Simplify the result using the exponent rule that any non-zero number raised to the power of 0 is 1

1

Final Answer

(lim_x→0)(ex)=1

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