Evaluate the Limit

Problem

(lim_x→∞)((x2+2*x−3)/(2*x2−2))

Solution

1. Identify the highest power of x in the denominator, which is x2

2. Divide every term in both the numerator and the denominator by x2 to prepare for the limit evaluation.

(lim_x→∞)(((x2)/(x2)+(2*x)/(x2)−3/(x2))/((2*x2)/(x2)−2/(x2)))

3. Simplify each term within the expression.

(lim_x→∞)((1+2/x−3/(x2))/(2−2/(x2)))

4. Apply the limit property that (lim_x→∞)(k/(xn))=0 for any constant k and n>0

(1+0−0)/(2−0)

5. Calculate the final numerical value.

1/2

Final Answer

(lim_x→∞)((x2+2*x−3)/(2*x2−2))=1/2

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