Calculus 1: Limits

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

##\lim_{x \rightarrow 4} \frac{x^2 - 16}{x - 4}##

##\lim_{x\rightarrow 9} \frac{\sqrt{x} - 3}{x - 9} ##

##\lim_{x\rightarrow -3} \frac{x^2 - x + 12}{x + 3}##

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

##\lim_{h\rightarrow 0} \frac{(h-5)^2 - 25}{h} ##

##\lim_{x\rightarrow 0} \frac{\sqrt{2 - x} - \sqrt{2}}{x}##

Use the squeeze theorem to prove the following important trigonometric limit
##\lim_{\theta\rightarrow 0} \frac{\sin(\theta)}{\theta} = 1##

##\lim_{ \theta\rightarrow 0} \frac{\cos(\theta) - 1}{\theta}##

Let ##g(x) = \frac{|x^2 + x - 6|}{x - 2} ##
Find the limit as ##x\rightarrow 2^{+} x\rightarrow 2^{-} x\rightarrow 2 ##

Let ## f(x) = \frac{3}{x - 5}##,
Evaluate the limit as ##x\rightarrow 5^{-}## and ## x\rightarrow 5^{+}##

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

##\lim_{x\rightarrow \infty}\frac{3x^2 - 5x + 1}{x^3 - 1} ##

##\lim_{x\rightarrow \infty} \frac{2x + 1}{\sqrt{x^2 - x}} ##

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

##\lim_{x\rightarrow \infty}(\frac{5}{x} - \arctan{x}) ##

##\lim_{x\rightarrow -\infty} \frac{x}{\sqrt{x^2 + 1}}##

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

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

##\lim_{x\rightarrow 0} \frac{\sin{(3x)}}{x} ##