Practice One-sided Limits (5) - Limits - IB 10 Mathematics

Practise this section

9 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Evaluate the left-hand limit: lim x→0⁻ (2x + 3)
Show hintHide hint
Substitute values slightly less than 0.
Question 2.
Evaluate the right-hand limit: lim x→1⁺ (x² - 1)
Show hintHide hint
Substitute values slightly greater than 1.
3Question 3.
What is a left-hand limit?
- lim x→a f(x)
- lim x→a⁻ f(x)
- lim x→a⁺ f(x)
Show hintHide hint
Think about approaching the point from the lower side.
4Question 4.
Does the limit exist where lim x→3⁻ f(x) = 1 and lim x→3⁺ f(x) = 2?
- True
- False
Show hintHide hint
Remember, for limits to exist, both sides must agree.
Question 5.
Prove that lim x→2⁻ (x² + 3) = 7 and lim x→2⁺ (x² + 3) = 7. What does this imply about lim x→2?
Show hintHide hint
Calculate both limits directly by substituting.
Question 6.
Consider the function f(x) = (x²-4)/(x-2). Determine the limits as x approaches 2 from both sides. What does this indicate about continuity?
Show hintHide hint
Factor the numerator and simplify.

5 more questions in this section. Enroll free to practise them all.