Finding Limits at Infinity

Calculus 1 · Axiom Academy

EXAMPLE Finding Limits at Infinity Divide the numerator and denominator by the highest power of x , send each , and read off the limit. Evaluate the limit of a rational function as x grows without bound: We will work it the systematic way — the same method handles any rational function at infinity. Nicely done. You evaluated a limit at infinity by dividing through by the highest power of x and letting every 1/x^n vanish. That single move settles any rational function — the degrees decide which of three things happens. A finite limit at infinity means the graph flattens toward a horizontal asymptote — here the line y = 3 .

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