Calculus Answers

Is the given linear expression a factor of the polynomial? Show your work.

13: f(x) = 2x^3 + x^2 -5x + 2
Yes

14: g(x) = 3x^3 + 2x^2 -17x + 6; x + 3
No

15: h(x) = x^4 -4x^3 -15x^2 + 58x -40; x – 5
yes

9: A computer can sort x objects in t seconds, as modeled by the function below:

t = 0.005x^2 + 0.002x

How many objects are required to keep the computer busy for exactly 9 seconds?

Round to the nearest whole object. Answer: ________

10: A computer can sort x objects in t seconds, as modeled by the function below:
t = 0.003x^2 + 0.001x

How long, in seconds will it take the computer to sort 12 objects?

Round your answer to the nearest hundredth of a second. Answer: ______

4: A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. What is the maximum height, in feet, the ball will attain?

Round to the nearest whole foot. Answer: _____

5: A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?

Round to the nearest hundredth. Answer: ____

6: The finishing time for a runner completing the 200-meter dash is affected by the tail-wind speed, s . The change, t, in a runner's performance is modeled by the function shown below:

t = 0.0119s^2 – 0.308s – 0.0003

Predict the change in a runner's finishing time with a wind speed of 5 meters/second. Note: A negative answer means the runner finishes with a lower time.

Round to the nearest hundredths. Answer: ____

7: Describe the Nature of the roots for this equation.
2x^2 + 5x – 7 = 0

A: one real, double root
B: Two complex roots.
C: Two real, rational roots
D: Two real, irrational roots.

8: Describe the nature of the roots for this equation.
x^2 -2x + 1 = 0

A: Two complex roots
B: One real, double root
C: Two real, rational roots
D: Two real, irrational roots

9: x^2 – 4x + 85 = 0

A: {2 + 19i, 2 – 19i}
B: {2 + 9i, 2 – 9i}
C: {7 +3i, 7 - 3i}
D: {3 + 7i, 3 – 7i}

10: A toy company has determined that the revenue generated by a particular toy is modeled by the following equation: r(x) 11x -0.025x^2

The variable x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars. What is the maximum revenue the company can earn with this toy?

Give the answer in dollars.

Answer:

differentiate the following(2x2−7)

8 Let f(x,y) be a real single-valued function of two independent variables x and y, then the partial derivatives of f(x,y) with respect to y is defined as
(A)lim dx→0 f(x+dx,y)−f(x,y)/dx (B) lim dx→0 f(x,y+dy)−f(x,y)/dy (C) lim dx→0 f(x+dx,y)−f(y,x)/dy (D) lim dx→0 f(x+dx,y+dy)−f(x,y)/dx
9 Let f(x,y) be a real single-valued function of two independent variables x and y, then the partial derivatives of f(x,y) with respect to x is defined as
(A) lim dx→0 f(x+dx,y)−f(x,y)/dx (B) lim dx→0 f(x+dx,y)−f(x,y)/dy (C) lim dx→0 f(x+dx,y)−f(y,x)/dx (D) lim dx→0 f(x+dy,y)−f(x,y)/dx

10 If f(x,y)=2x^3 +3y^2, find f(-1,-2)

2 If f(x,y)=tan^ −1 y/x, find f x.
3 Suppose f(x,y) =x^3 y^ 2 –sin^ 2xcos2y, what is ∂f/∂y?
4 Suppose f(x,y)=sin^2xcosy+xy^ 2, what is ∂f/∂x ?
5 If f(x,y)=x^ 2 y^ 3 –2y^ −2, find f y
6 If f(x,y)=4x^3 –3y^2, find f x

: For the sequence given by an = 4n + 5, answer the following: Note in the an the n is little.

a. Find the first five terms.

b. Find the sum of the first 25 terms.

c. Is this an arithmetic sequence? And how.




: Graph the area bounded by y < ½ x + 6, x + 3y ≥ 12, x≥ 0, and x ≤ 12.

: For the function defined by. { x^2 , x≤ 1 }
f(x) = {2x +1, x > 1}

a. Evaluate f(0)

b. Graph f(x)

If f and g are two functions of x, then …………….

A. d/dx (f/g )=fdf/dx –gdg/dx/ f ^2

B. d/dx (f/g )=gdf/dx –fdg/dx/ f ^2

C. d/dx (f/g )=gdfdx –fdfdx/ g^ 2

D. d/dx (f/g )=gd/fdx –fdg/dx/ g^ 2

3 If f(x) is a function of x and df/dx exists at x = a, then f(x) is
A. continuous at x = 0 B.discontinuous at x = 0 C. continuous at x = a D. discontinuous at x = a

5. If y = arcsin x, then d/dx (y) is
6 If y = arcsin x, then dx/dy is
7 If y = arcsin x, then x is