22 calculus questions

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1.

Use your graphing calculator to evaluate limit as x goes to infinity of the quantity 1 plus x raised to the power of 3 divided by x . (2 points)


2.

Use your calculator to select the best answer below:

limit as x goes to infinity of the quotient of the quantity the natural log of the absolute value of x minus 1 and the quantity cosine x raised to the x power (2 points)



3.

limit as x approaches a of the quotient of the quantity a minus x and the quantity the square root of x minus the square root of a equals (2 points)



4.

Find the limit as x goes to 0 of the quotient of the quantity 4 times x plus 1 minus the square of cosine x and the sine of x . (2 points)



5.

If limit as x approaches zero of f of x equals two and limit as x approaches zero of g of x equals six , then find limit as x approaches zero of the quantity f of x plus g of x squared . (2 points)



6.

Evaluate limit as x approaches 2 of the quotient of the absolute value of the quantity x minus 2 and x minus 2 . (2 points)



7.

Evaluate limit as x goes to 4 of the quotient of the quantity 1 divided by x minus 1 over 4 and the quantity x minus 4 . (2 points)



8.

Evaluate limit as x goes to 0 of the quotient of the sine of 5 times x and 6x . (2 points)



9.

If f is a continuous function with odd symmetry and limit as x approaches infinity of f of x equals 6 , which of the following statements must be true? (2 points)

I. the limit as x goes to negative infinity of f of x equals negative 6

II. There are no vertical asymptotes.

III. The lines y = 6 and y = -6 are horizontal asymptotes



10.

What are the horizontal asymptotes of the function f of x equals the quotient of 5 times the square root of the quantity x squared plus 9 and x ? (2 points)



11.

Which one or ones of the following statements is/are true? (2 points)

I. If the line y = 2 is a horizontal asymptote of y = f(x), then f is not defined at y = 2.

II. If f(5) > 0 and f(6) < 0, then there exists a number c between 5 and 6 such that f(c) = 0.

III. If f is continuous at 2 and f(2)=8 and f(4)=3, then the limit as x approaches 2 of f of the quantity 4 times x squared minus 8 equals 8 .



12.

Find limit as x goes to infinity of the quotient of 4 times x squared squared plus 8 times x and x cubed plus 7 times x squared minus x minus 9 (2 points)



13.

Evaluate limit as x goes to 2 from the right of the quotient of x and the quantity the square root of the quantity x squared minus 4 . (2 points)



14.

Which of the following are the equations of all horizontal and vertical asymptotes for the graph of f of x equals x divided by the quantity x times the quantity x squared minus 9 ? (2 points)



15.

Evaluate limit as x approaches 2 at f of x for f of x equals the quantity 2 times x minus 1 for x less than 2, equals 1 for x equals 2 and equals x plus 6 for x greater than 2 . (2 points)



16.

Where is f of x equals the quotient of x plus 2 and x squared minus 2 times x minus 8 discontinuous? (2 points)



17.

Which of the following are continuous for all real values of x? (2 points)

I. f of x equals the quotient of the quantity x squared plus 5 and the quantity x squared plus 1

II. g of x equals the quotient of 3 and x squared

III. h of x equals the absolute value x



18.

Which of the following must be true for the graph of the function f of x equals the quotient of the quantity x squared minus 9 and the quantity 3 times x minus 9 ? (2 points)

There is:

I. a vertical asymptote at x = 3

II. a removable discontinuity at x = 3

III. an infinite discontinuity at x = 3



19.

What is the average rate of change of y with respect to x over the interval [1, 5] for the function y = 4x + 2? (2 points)



20.

What is the instantaneous slope of y = negative seven over x at x = 3? (2 points)



21.

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 128 feet high is s(t) = -16t2 – 32t + 128, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? (2 points)



22.

The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4. (2 points)


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