Evaluate the Limit limit as x approaches -2 of 1/(x+3)

Problem

(lim_x→−2)(1/(x+3))

Solution

1. Identify the type of function. The expression 1/(x+3) is a rational function.

2. Check for continuity at the target value. A rational function is continuous at all points in its domain, which includes any x where the denominator is not zero.

3. Evaluate the denominator at x=−2 Since −2+3=1 which is not zero, the function is continuous at x=−2

4. Substitute the value x=−2 directly into the expression to find the limit.

L=1/(−2+3)

5. Simplify the resulting fraction.

L=1/1

L=1

Final Answer

(lim_x→−2)(1/(x+3))=1

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