Still Confused?

Try reviewing these fundamentals first.

- Home
- Sixth Year Maths
- Limits

Still Confused?

Try reviewing these fundamentals first.

Nope, I got it.

That's that last lesson.

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Lesson: 110:24
- Lesson: 23:55
- Lesson: 3a7:25
- Lesson: 49:43
- Lesson: 510:17

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.

- 1.
**Simplify Out "Zero Denominator" by Cancelling Common Factors**Find $\lim_{x \to 3} \;\frac{{{x^2} - 9}}{{x - 3}}$

- 2.
**Expand First, Then Simplify Out "Zero Denominator" by Cancelling Common Factors**Evaluate $\lim_{h \to 0} \;\frac{{{{\left( {5 + h} \right)}^2} - 25}}{h}$

- 3.
**Simplify Out "Zero Denominator" by Rationalizing Radicals**Evaluate:

a)$\lim_{x \to 4} \;\frac{{4 - x}}{{2 - \sqrt x }}$*(hint: rationalize the denominator by multiplying its conjugate)* - 4.
**Find Limits of Functions involving Absolute Value**Evaluate $\lim_{x \to 0} \;\frac{{\left| x \right|}}{x}$

*(hint: express the absolute value function as a piece-wise function)* - 5.
**Find Limits Using the Trigonometric Identity:$\lim_{\theta \to 0} \;\frac{{{sin\;}\theta}}{{\theta}}=1$**Find $\lim_{x \to 0} \;\frac{{{sin\;}5x}}{{2x}}$

23.

Limits

23.1

Finding limits from graphs

23.2

Limit laws

23.3

Continuity

23.4

Finding limits algebraically - direct substitution

23.5

Finding limits algebraically - when direct substitution is not possible

23.6

Infinite limits - vertical asymptotes

23.7

Limits at infinity - horizontal asymptotes

23.8

Intermediate value theorem

23.9

Squeeze theorem

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now23.1

Finding limits from graphs

23.3

Continuity

23.4

Finding limits algebraically - direct substitution

23.5

Finding limits algebraically - when direct substitution is not possible

23.6

Infinite limits - vertical asymptotes

23.7

Limits at infinity - horizontal asymptotes

23.8

Intermediate value theorem

23.9

Squeeze theorem