Finding limits from graphs

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

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