Section 2.3 Examples
Evaluate the limit, if it exists.
1. \(\displaystyle \lim_{x\rightarrow 2} \, (x^3-3x^2+5) \)

Solution


2. \(\displaystyle \lim_{x\rightarrow 3 }\frac{x^2-9}{x-3}\)

Solution


3. \(\displaystyle \lim_{x\rightarrow \frac{\pi}{2}}\frac{\sin{x}}{\cos{2x}}\)

Solution


4. \(\displaystyle \lim_{x\rightarrow -3}\frac{x^3-2x^2-15x}{x^2+x-6}\)

Solution


5. \(\displaystyle \lim_{t\rightarrow 1 }\frac{t^2+t-2}{t^4-1}\)

Solution


6. \(\displaystyle \lim_{h\rightarrow 0}\frac{\sqrt{16+h}-4}{h}\)

Solution


7. \(\displaystyle \lim_{u \rightarrow 4}\frac{\sqrt{2u+1}-3}{u^2-4u}\)

Solution