Mathematics – Calculus assignment
There is 18 multiple choice questions. READ the choices given carefully because they are cut off. Highlight the right question in yellow. Answer only one question.
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
· 5×2 – 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).
