Finding limits from graphs

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/5
?
Examples
Lessons
  1. For the function f whose graph is shown, state the following:
    Finding limits from graphs
    1. limx5f(x)\lim_{x \to -5^-} f(x)
      limx5+f(x)\lim_{x \to -5^+} f(x)
      limx5f(x)\lim_{x \to -5} f(x)
      f(5)f(-5)
    2. limx2f(x)\lim_{x \to -2^-} f(x)
      limx2+f(x)\lim_{x \to -2^+} f(x)
      limx2f(x)\lim_{x \to -2} f(x)
      f(2)f(-2)
    3. limx1f(x)\lim_{x \to 1^-} f(x)
      limx1+f(x)\lim_{x \to 1^+} f(x)
      limx1f(x)\lim_{x \to 1} f(x)
      f(1)f(1)
    4. limx4f(x)\lim_{x \to 4^-} f(x)
      limx4+f(x)\lim_{x \to 4^+} f(x)
      limx4f(x)\lim_{x \to 4} f(x)
      f(4)f(4)
    5. limx5f(x)\lim_{x \to 5^-} f(x)
      limx5+f(x)\lim_{x \to 5^+} f(x)
      limx5f(x)\lim_{x \to 5} f(x)
      f(5)f(5)
Topic Notes
?
Limit is an important instrument that helps us understand ideas in the realm of Calculus. In this section, we will learn how to find the limit of a function graphically using one-sided limits and two-sided limits.
DEFINITION:
left-hand limit: limxaf(x)=L\lim_{x \to a^-} f(x) = L
We say "the limit of f(x), as x approaches a from the negative direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the left, but x is not equal to a.

DEFINITION:
right-hand limit: limxa+f(x)=L\lim_{x \to a^+} f(x) = L
We say "the limit of f(x), as x approaches a from the positive direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the right, but x is not equal to a.

DEFINITION:
limxaf(x)=L\lim_{x \to a} f(x) = L if and only if limxa+f(x)=L\lim_{x \to a^+} f(x) = L and limxaf(x)=L\lim_{x \to a^-} f(x) = L