Finding limits algebraically - when direct substitution is not possible - Limits

Finding limits algebraically - when direct substitution is not possible

There are times when applying direct substitution would only give us an undefined solution. In this section, we will explore some cool tricks to evaluate limits algebraically, such as using conjugates, trigonometry, common denominators, and factoring.

Lessons

  • 3.
    Simplify Out "Zero Denominator" by Rationalizing Radicals

    Evaluate:

    • b)
      limx7x+23x7\lim_{x \to 7} \;\frac{{\sqrt {x + 2} - 3}}{{x - 7}}
      (hint: rationalize the numerator by multiplying its conjugate)
Teacher pug

Finding limits algebraically - when direct substitution is not possible

Don't just watch, practice makes perfect.

We have over 350 practice questions in Calculus for you to master.