Practice Concept Of Limit (4.2.1) - Calculus

Practise this section

9 questions

Flashcard drill
3 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.
What is the limit of f(x) = 3x as x approaches 1?
Show hintHide hint
Simply substitute x = 1 into the function.
Question 2.
True or False: Limits can be used to find the value of functions at points where they are undefined.
Show hintHide hint
Think about how limits work with functions.
3Question 3.
What does the limit of a function as x approaches a indicate?
- The function's value at a.
- What the function approaches near a.
- The behavior of the function at infinity.
Show hintHide hint
Think about what happens to the function as it gets close to a.
4Question 4.
True or False: The limit can help define continuity at a point.
- True
- False
Show hintHide hint
Consider the relationship between limits and continuity.
Question 5.
Using epsilon-delta definitions, prove that lim(x→a) f(x) = L for a specific function f(x).
Show hintHide hint
Start by assuming |f(x) - L| < epsilon when |x-a| < delta.
Question 6.
Evaluate the limit lim(x→a) (x^3 - a^3)/(x-a).
Show hintHide hint
Factor the numerator and simplify before substituting.

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