Evaluate the Limit

Problem

(lim_x→∞)((5*x−3)/(2*x^2+2*x+4))

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 simplify the expression for the limit at infinity.

(lim_x→∞)(((5*x)/(x^2)−3/(x^2))/((2*x^2)/(x^2)+(2*x)/(x^2)+4/(x^2)))

3. Simplify each individual term within the fraction.

(lim_x→∞)((5/x−3/(x^2))/(2+2/x+4/(x^2)))

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

(0−0)/(2+0+0)

5. Evaluate the resulting numerical expression.

0/2=0

Final Answer

(lim_x→∞)((5*x−3)/(2*x^2+2*x+4))=0

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