Evaluate the Limit

Problem

(lim_x→∞)((x^2+2*x−3)/(2*x^2−2))

Solution

1. Identify the highest power of x in the denominator, which is x^2

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

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

3. Simplify each term within the expression.

(lim_x→∞)((1+2/x−3/(x^2))/(2−2/(x^2)))

4. Apply the limit property that (lim_x→∞)(k/(x^n))=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→∞)((x^2+2*x−3)/(2*x^2−2))=1/2

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