Evaluate the Limit

Problem

(lim_h→0)((2*(x+h)−2*x)/h)

Solution

1. Distribute the constant 2 into the parentheses in the numerator.

(2*x+2*h−2*x)/h

2. Simplify the numerator by combining the like terms 2*x and −2*x

(2*h)/h

3. Divide the numerator and denominator by h noting that h≠0 as it approaches 0

2

4. Evaluate the limit of the resulting constant.

(lim_h→0)(2)=2

Final Answer

(lim_h→0)((2*(x+h)−2*x)/h)=2

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