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  2. AP Calculus
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Limits and Continuity

Question 1
college-boardCalculus AB/BCAPExam Style
1 mark

What type of discontinuity does a function have if it approaches a vertical asymptote at a certain point?

Question 2
college-boardCalculus AB/BCAPExam Style
1 mark

For the function h(x)=e−∣ax∣h(x)=e^{-|ax|}h(x)=e−∣ax∣ where aaa is a positive constant, what is the effect on the horizontal asymptote when aaa is incrementally increased?

Question 3
college-boardCalculus AB/BCAPExam Style
1 mark

What type of discontinuity does the function have if the left and right-handed limits are not equal?

Question 4
college-boardCalculus AB/BCAPExam Style
1 mark

If the left-handed limit of a function at a certain point is 5 and the right-handed limit is 3, what type of discontinuity does the function have at that point?

Question 5
college-boardCalculus AB/BCAPExam Style
1 mark

What type of discontinuity is present at a point where the left and right-hand limits exist and are equal, but the function value is not defined?

Question 6
college-boardCalculus AB/BCAPExam Style
1 mark

The piecewise function defined by h(x)={x+1x<0x2x≥0h(x) = \begin{cases} x + 1 & x < 0 \\ x^2 & x \geq 0 \end{cases}h(x)={x+1x2​x<0x≥0​ exhibits which kind of behavior as it approaches zero from both sides?

Question 7
college-boardCalculus AB/BCAPExam Style
1 mark

Which type of singularity might arise in real analysis such that near this singular point, despite being able to define values arbitrarily close on either side, a unique tangent cannot be determined due to erratic oscillation?

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Question 8
college-boardCalculus AB/BCAPExam Style
1 mark

If a function approaches closer and closer to a certain value but never reaches it, what type of discontinuity does it have?

Question 9
college-boardCalculus AB/BCAPExam Style
1 mark

For a rational function with a removable discontinuity at x=ax=ax=a, what will be the effect on this discontinuity if we multiply our function by sin⁡(πx)\sin(\pi x)sin(πx)?

Question 10
college-boardCalculus AB/BCAPExam Style
1 mark

The graph of a rational function has a vertical asymptote at x=−4x=-4x=−4. Which type of discontinuity is represented by this vertical asymptote?