IB Mathematics Analysis and Approaches Question Type 1: Simple Limits: Convergence, Divergence, and Function Behavior Exercises

Find $\underset{x\to \infty }{\lim }\frac{5x^2+3x}{2x^2-x}$.

Determine $\underset{x\to \infty }{\lim }\frac{2x^3-x}{x^2+1}$.

Evaluate $\underset{x\to 3}{\lim }\frac{x^2-9}{x-3}$.

Compute $\underset{x\to -\infty }{\lim }\frac{x^3-2x}{x^2+1}$.

Find $\underset{x\to -2}{\lim }\frac{x^2+3x+2}{x+2}$.

Compute $\underset{x\to 0}{\lim }\frac{\sin x}{x}$.

Determine $\underset{x\to 2}{\lim }\frac{3x+5}{x-2}$.

Evaluate $\underset{x\to 1}{\lim }\frac{x^3-1}{x-1}$.

Calculate $\underset{x\to 0}{\lim }\frac{x^3+4x}{3x^3+1}$.

Determine $\underset{x\to \pi }{\lim }\frac{\sin x}{x-\pi }$.

Find $\underset{x\to 0}{\lim }\frac{e^x-1}{x}$.

Find $\underset{x\to -1}{\lim }\frac{x^2-1}{x+1}$.