Limits at infinity
Limits and continuity · Mathematics
Study notes
Q: Evaluate: (a) lim(x→∞) (3x²+2x)/(5x²−1) (b) lim(x→∞) (x³+1)/(x²+1). (a) Divide by x²: (3+2/x)/(5−1/x²) → 3/5. (b) Divide by x²: (x+1/x²)/(1+1/x²) → ∞. (Numerator degree wins.)
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Limits and continuity · Mathematics
Q: Evaluate: (a) lim(x→∞) (3x²+2x)/(5x²−1) (b) lim(x→∞) (x³+1)/(x²+1). (a) Divide by x²: (3+2/x)/(5−1/x²) → 3/5. (b) Divide by x²: (x+1/x²)/(1+1/x²) → ∞. (Numerator degree wins.)