AP Calculus AB Questions

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Home>Mathematics homework help>Calculus homework help>AP Calculus AB Questions

1. 

Use your graphing calculator to evaluate limit as x goes to infinity of the quantity 1 plus x all raised to the power of 2 divided by x .

 

· 0

· π

· e2

· 1

2. 

Describe the discontinuity for the function f of x equals the quotient of the quantity x squared plus 16 and the quantity x minus 4 .

 

· There is no discontinuity at x = 4.

· There is a hole at x = -16.

· There is a removable discontinuity at x = 4.

· There is a vertical asymptote at x = 4.

3. 

Find limit as x goes to 0 of the quotient of the sine of negative 6 times x and the sine of negative 5 times x .

 

· 5 over 6

· 6 over 5

· does not exist

· 0

4. 

Evaluate limit as x goes to negative 1 from the left of the quotient of x and the quantity x plus 1 .

 

· -∞

· 0

· -1

· ∞

5. 

Evaluate limit as x goes to infinity of the quotient of the quantity negative x cubed minus 2 times x squared minus 7 times x and the quantity negative 3 times x squared minus 4 times x minus 8 .

 

· 1 over 3

· ∞

· 0

· -∞

6. 

Which of the following is the graph of which function has y = -1 as an asymptote?

 

· y equals negative x divided by the quantity 1 minus x

· y = ln(x + 1)

· y equals x divided by the x plus 1

· y equals x divided by the quantity 1 minus x

7. 

If f of x equals the quotient of the quantity x squared minus 16 and the quantity x plus 4 is continuous at x = -4, find f(-4).

 

· 4

· -4

· 8

· -8

8. 

Where is f of x equals the quotient of the quantity x minus 5 and x squared minus 3 times x minus 10 discontinuous?

 

· f(x) is continuous everywhere

· x = 5

· x = 5 and x = -2

· x = -2

9. 

If f(x) is discontinuous, determine the reason.

f of x equals the quantity x squared plus 4 for x less than or equal to 1 and equals x plus 4 for x greater than 1 (5 points)

 

· f(x) is continuous for all real numbers

· The limit as x approaches 1 does not exist

· f(1) does not equal the limit as x approaches 1

· f(1) is not defined

10. 

If f(x) is a continuous function defined for all real numbers, f(-10) = -2, f(-8) = 5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value?

 

·

· -7

·

· -9

·

· 0

·

· 2

11. 

Which one of the following is a function?

 

· 5x - 2y = 10

· 5x - 2y2 = 9

· 5x2 - 2y2 = 9

12. 

Determine the range of f(x) = 3(x - 2)2 + 3.

 

· All real numbers

· y ≥ 3

· y > 3

· y ≥ 0

13. 

Find the domain of f(x) = the square root of square of the quantity x plus 2.

 

· x > 2

· x > -2

· x ≥ -2

· All real numbers

14. 

Find the domain for the function f(x) =the quotient of the square root of the quantity x plus 5 and the quantity x minus 1.

 

· x ≠ 1

· x ≥ -5

· x ≥-5, x ≠ 1

· All real numbers

15. 

Which of the following statements are true about functions and relations?

 

·

· The vertical line test will not work for piece-wise defined relations.

·

· No piece-wise relations can be functions.

·

· The vertical line test must only cross the curve one place for each x value for an function.

·

· The vertical line test can cross the curve at more than one place for each x value for a function.

16. 

Evaluate limit as x goes to infinity of the quotient of 4 times x cubed plus 2 times x squared plus 3 times x and negative 9 times x squared plus 5 times x plus 5 

 

·

· ∞

·

· -∞

·

· 0

·

· 4 over 9

17. 

Find the equation of the horizontal asymptote for the function, f of x equals the quotient of the quantity x raised to the 10th power minus 1 and x minus 1 .

 

· y = 10

· y = 0

· y = 9

· There is no horizontal asymptote.

18. 

Which of the following is false for f of x equals the quotient of 3 times x cubed minus 3 times x squared minus 6 times x and the quantity 2 times x raised to the fifth power minus 2 times x ?

 

· x = 1 is an asymptote of f(x).

· The y-axis is an asymptote of f(x).

· The x-axis is an asymptote of f(x).

· x = -1 is not an asymptote of f(x).