Evaluate the Limit limit as x approaches 5 of -2/2*(12x-8)

Problem

(lim_x→5)((−2)/2)*(12*x−8)

Solution

1. Simplify the constant coefficient outside the parentheses by dividing −2 by 2

(−2)/2=−1

2. Rewrite the limit expression using the simplified constant.

(lim_x→5)(−)*1*(12*x−8)

3. Apply the direct substitution property for limits of polynomial functions by substituting x=5 into the expression.

−1*(12*(5)−8)

4. Calculate the value inside the parentheses by performing the multiplication and then the subtraction.

12⋅5=60

60−8=52

5. Multiply the result by the constant −1 to find the final limit value.

−1⋅52=−52

Final Answer

(lim_x→5)((−2)/2)*(12*x−8)=−52

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