Evaluating limits analytically

Polynomial function P(x)
 $\lim_{x\rightarrow c}P\left(x\right)=P\left(c\right)$ 
(check the appropriate box)

• Always

• Sometimes

• Never

A limit (if it exists) is a(n)

• x-value at a point

• y-value at a point

• point (x , y)

• indeterminable form

Which of the following limits can be found by direct substitution?

(check all that apply)

• $\lim_{x\rightarrow5}\left(4x+9\right)$

• $\lim_{x\rightarrow12}\frac{x^2-144}{x-12}$

• $\lim_{x\rightarrow\frac{\pi}{3}}\cos\left(x\right)$

• $\lim_{x\rightarrow7}\frac{\sqrt{x+18}-5}{x-7}$

Evaluate
 $\lim_{x\rightarrow\frac{5\pi}{4}}\left[\cot\left(x\right)\sin\left(x\right)\right]$ 

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{\sqrt{2}}{2}$  

•  $-\ \frac{\sqrt{3}}{2}$  

•  $-\ \frac{\sqrt{2}}{2}$  

 $\lim_{x\rightarrow1}^{ }x^3+3x^2-2x$  

 $\lim_{x\rightarrow-3}\frac{x^2+4x+3}{x^2-3}$  

 $\lim_{x\rightarrow1}\frac{x-1}{x^2-1}$  

 $\lim_{x\rightarrow2}\frac{x^2-3x+2}{x^2-4}$  

 $\lim_{x\rightarrow0}\frac{\left(4+x\right)^2-16}{x}$  

 $\lim_{x\rightarrow0}\frac{5x^3+8x^2}{3x^4+12x^2}$