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

Limits and Continuity

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

If the limit of a function as x approaches a certain value is equal to the value of the function at that point, what can be concluded?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

What is the limit as x approaches zero of function h(h) = 5/x?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

What does the limit of a function represent as x approaches infinity?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

What is the value of lim⁡x→3x2−9x−3\displaystyle\lim_{x \to 3} \frac{x^2 - 9}{x-3}x→3lim​x−3x2−9​?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

What must be true about f(x) if lim⁡x→af(x)\lim_{x \to a} f(x)limx→a​f(x) exists and is finite?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

What does it mean if the limit of a function does not exist?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

What is the limit of the function f(x)=sin⁡(x)xf(x) = \frac{\sin(x)}{x}f(x)=xsin(x)​ as xxx approaches 0?

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

Which statement correctly describes an important aspect regarding one-sided limits?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

Which expression is equivalent to the statement "the limit of f(x), as x approaches two from the left side"?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

Given that lim⁡h→0f(3+h)−f(3)h=6\lim_{h \to 0} \frac{f(3+h)-f(3)}{h} = 6limh→0​hf(3+h)−f(3)​=6, what is f'(3)?