Limit laws

Lessons

• Introduction
  Limit Laws Overview:
  7 Properties of Limit Laws

---

• 1.
  Evaluating Limits of Functions
  Evaluate the following limits using the property of limits:
  a)

  $\lim_{x \to 2} x^2+4x+3$
  
  
  b)

  $\lim_{x \to 2} 3(x^2+4x+3)^2$
  
  
  c)

  $\lim_{x \to 1} \frac{2-3x+4x^2}{2+x^4}$
  
  
  d)

  $\lim_{x \to 0} 4(3)^x$
  
  
  e)

  $\lim_{x \to \frac{\pi}{2}} 3(\sin x)^4$
  
  

---

• 2.
  Evaluating Limits with specific limits given
  Given that $\lim_{x \to 5} f(x)=-3$, $\lim_{x \to 5} g(x)=5$, $\lim_{x \to 5} h(x)=2$, use the limit properties to compute the following limits:
  a)

  $\lim_{x \to 5} [5f(x)-2g(x)]$
  
  
  b)

  $\lim_{x \to 5} [g(x)f(x)+3h(x)]$
  
  
  c)

  $\lim_{x \to 5} \frac{2g(x)}{h(x)}$
  
  
  d)

  $\lim_{x \to 5} \frac{5[f(x)]^3}{g(x)}$
  
  

---