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Calculus 1: Limits

limx3(2x+5)\lim_{x \to 3} (2x + 5)

limt1t3tt21\lim_{t \rightarrow 1} \frac{t^3 - t}{t^2 - 1}

limh0(h5)225h\lim_{h\rightarrow 0} \frac{(h-5)^2 - 25}{h}

Use the squeeze theorem to prove the following important trigonometric limit

limθ0sin(θ)θ=1\lim_{\theta\rightarrow 0} \frac{\sin(\theta)}{\theta} = 1

limx2x1x+1\lim_{x\rightarrow \infty}\frac{2x - 1}{x + 1}

limsin1x\lim_{\rightarrow \infty}\sin\frac{1}{x}

limθ0sec(2θ)tan(3θ)5θ\lim_{\theta\rightarrow 0} \frac{\sec{(2\theta)} \tan{(3 \theta)}}{5 \theta}

limx0tanxx\lim_{x\rightarrow 0} \frac{\tan{x}}{x}