Evaluate the Limit limit as x approaches 0 of -5/2*(10x-20)

Problem

(lim_x→0)(−)5/2*(10*x−20)

Solution

1. Identify the type of limit. Since the expression −5/2*(10*x−20) is a linear polynomial, it is continuous everywhere.

2. Apply the direct substitution property for limits of continuous functions by substituting x=0 into the expression.

3. Substitute the value of x into the function:

−5/2*(10*(0)−20)

4. Simplify the expression inside the parentheses:

−5/2*(0−20)

−5/2*(−20)

5. Calculate the final product:

(−5⋅−20)/2

100/2

50

Final Answer

(lim_x→0)(−)5/2*(10*x−20)=50

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