AP Calculus AB #1

That's rights, you calculus crazies. As I learn, I also help! Enjoy this quiz about limits and an intro to derivatives. Good luck! (It's super easy. I didn't try hard.)

Quiz by

Rate:

Last updated: September 19, 2023

You have not attempted this quiz yet.

More quiz info >>

First submitted	September 19, 2023
Times taken	117
Average score	50.0%
Report this quiz	Report

Quiz and answer stats >>

Friends stats >>

4:00

The quiz is paused. You have remaining.

Scoring
You scored / = %

      This beats or equals
      % of test takers
      also scored 100%
      
The average score is 

        Your high score is
        
      
Your fastest time is 
more stats >>
friends stats >>

Keep scrolling down for answers and more stats ...

1. lim x->9 (8x) Continuous or discontinuous?

Infinite Discontinuity ✓

Continuous ✓

Jump Discontinuity ✓

Removable Discontinuity ✓

2. If a piecewise function has f(x) values defined for only x<6 and x>6 then is it continuous?

Continuous ✓

Removable Discontinuity ✓

Jump Discontinuity ✓

Infinite Discontinuity ✓

3. Which of the following functions have two infinite x and y discontinuities, each the same value?

x/2 ✓

1/x ✓

x^2 ✓

2x-5 ✓

4. Which of the following is a method of algebraically finding the a- and a+ limits of a function with a jump discontinuity, given that x=a?

You can't determine the limit(s) only given the function, more information is needed. ✓

Use the conjugate method, in which you multiply each part of the fraction by a certain number that simplifies the fraction to something that you can evaluate. ✓

Use the plugin method, plug in a into the function, and the limit is the answer you get from it. ✓

Use a table, creating a list of x-values from each side of a that get closer and closer to a, and by plugging them into the function, you can get an answer that approximates the limits of both sides. ✓

5. How can you best algebraically evaluate limits that have radicals in them?

Use a calculator and evaluate the radical to the nearest tenth, then evaluate the rest of the function. ✓

Plug it in, it will yield an answer that you can evaluate using multiplication of radicals that produces a whole number answer. ✓

Use the conjugate method by multiplying the numerator and denominator by a certain number that simplifies the fraction to something you can evaluate without getting an undefined. ✓

Factor out the equation until you get pairs of binomials that you can remove holes from, and then evaluate the function. ✓

6. What is the limit of (5x^3-7)/(2x^3+5) as x approaches infinity?

infinity ✓

0 ✓

-5/2 ✓

5/2 ✓

7. How do we algebraically evaluate the limits of functions approaching infinity?

Rule out all unneeded constants and smaller terms and evaluate the term(s) with the degree of the equation. ✓

Plug in infinity and approximate a value that would lead to an accurate answer. ✓

Use the rule of infinites, where the limit of all functions approaching infinity would be infinity. ✓

Divide the two expressions and the result would be the limit. ✓

8. What is a secant line of a function?

Any line between two points on a function ✓

The trigonometric secant of the two highest points on a function ✓

The slope of the line that represents the secant of the lowest point on the function ✓

A line that only touches one point on a function ✓

9. What is a tangent line of a function?

Doesn't exist ✓

Any line between two points on a function ✓

The line that touches exactly one point on a function ✓

The tangent of the lowest point of a function ✓

10. What is a cosecant line of a function?

The line that touches only the lowest point of a function ✓

The backup secant line of a function ✓

A line that doesn't go until x = infinity ✓

Doesn't exist ✓

1 Comments

Show comments >

Level 53

Nov 27, 2023

I don't think the questions are well worded. You ask if a limit is "continuous" or "discontinuous" in the first one. Its should be "exists" or "does not exist".