zuai-logo
zuai-logo
  2. AP Calculus
FlashcardFlashcardStudy GuideStudy GuideQuestion BankQuestion Bank

Limits and Continuity

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

What is a leading term?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

For the function g(x)=5x−2g(x) = \frac{5}{x -2}g(x)=x−25​, what does lim⁡x→∞g(x)\lim_{x \to \infty} g(x)limx→∞​g(x) represent in terms of graph features?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

If lim⁡x→∞f(x)=L\lim_{x \to \infty} f(x) = Llimx→∞​f(x)=L, where L is a real number, what can be said about a possible horizontal asymptote of f(x)f(x)f(x)?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

When evaluating a limit at infinity for a rational function like x2+mx+nax+b\frac{x^2 + mx + n}{ax+b}ax+bx2+mx+n​ where m, n, a, b are constants with a ≠ 0, what characteristic determines if there's a horizontal asymptote?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

What is the limit of the function f(x)=100x+2x7f(x) = 100x + 2x^7f(x)=100x+2x7 as x approaches negative infinity?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

What does lim⁡x→−∞x3−x+45x3+7\lim_{x \to -\infty} \frac{x^3 - x + 4}{5x^3 + 7}limx→−∞​5x3+7x3−x+4​ equal to indicate about its graph as x becomes very negative?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

When evaluating lim⁡x→∞h(x)\lim_{x \to \infty} h(x)limx→∞​h(x) for some polynomial h(x)h(x)h(x), what result would suggest that h(x)h(x)h(x) has no horizontal asymptote?

Feedback stars icon

How are we doing?

Give us your feedback and let us know how we can improve

Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

For a rational function, when does a nonzero constant divided by an expression containing a variable raised to any power approach zero as that variable approaches infinity?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

If lim⁡x→−∞g(x)=−5\lim_{x \to -\infty} g(x) = -5limx→−∞​g(x)=−5, what does this tell us about the end behavior of g(x)g(x)g(x)?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

If the function 3x2+1x2−4\frac{3x^2 + 1}{x^2 - 4}x2−43x2+1​ has a horizontal asymptote, what is its equation as xxx approaches infinity?