Calculus Answers

Integrate the following functions w.r.t. x:

1. 1/(2x+1)^3/2

2. Sin(2x+3)

3. Cosec(4x)

4. 1/(1-9x²)^1/2

Find a formula an for the nth term of the arithmetic sequence whose first term is a1=−3 such that an+1−an=4 for n≥1.

Find the extreme values of f(x,y)=x^2+y on the surface x^2+y^2=1.

integrate (1-2x)/(45+4x-x^2) dx without using trig substitution

If this is the graph of f(x) = a^(x+h) + k then

1. Determine the first order partial derivative of the following functions:

a. z = In (x + t^2)

b. F(x,y,z) = xy^2 e^-xz

2. Clairaut's Theorwm holds that Uxy = Uyx , show that the following equations obey Clairaut's Theorem:

a. U = In( x+2y)

b. U = e^xy sin y

3. Laplaces equation holds that Uxx + Uyy= 0, verify that the second derivative of the following equations are Laplace's equations:

a. U = In√x^2 + y^2

b. U = x^2 - y^2

Which statement is correct about the system of inequalities x+2/y < 1 and y−7 > 5?

• The set of all ordered pairs whose x-coordinate is in the interval (−∞,10) and whose y-coordinate is in (12,∞) is part of the complete solution for the system.

• The set of all ordered pairs whose x-coordinate is in the interval (−∞,10) and whose y-coordinate is in (5,∞) is part of the complete solution for the system.

• The set of all ordered pairs whose x-coordinate is in the interval (−∞,1) and whose y-coordinate is in (5,∞) is the complete solution for the system.

• The set of all ordered pairs whose x-coordinate is in the interval (10,∞) and whose y-coordinate is in (12,∞) is the complete solution for the system.

Lorena is comparing the winning percentages of two baseball teams. The Scorpions have won 20

20 out of 35 games. The Iguanas have won 10 out of 34 games. There are x games remaining until the playoffs. Which rational equation correctly describes the event in which the Iguanas win y of the remaining games and reach the same winning percentage as the Scorpions?

Assume that the Scorpions do not win another game. 

• 10+x/34+x = 20/35+y
• 10+y/34+x = 20+y/35+x
• 10+y/34+y = 20+x/35+x
• 10+y/34+x = 20/35+x
• 10+y/34+x = 20+x/35+x

it's NOT: 10+x/34+x = 20/35+y

Use the inequality x^4+3x^3−2x^2−6 > 0 and a graphing calculator, or another piece of technology, to answer Part A and Part B.

Part A: What are the zeros of the inequality to the nearest hundredth?

Part B: What is the solution set for the inequality?

Select all possible answers for Part A and one answer for Part B.

B: (−∞,−3.67)∪(1.3,∞)

B: (−3.67,−1.3)∪(0,1.3)

B: (−∞,−3.67]∪(−1.3,0)∪[1.3,∞)

A: x≈1.3

A: x≈3.67

A: x≈−0.9

A: x≈−3.67

A: x≈−1.3

A: x≈0

Use a graphing calculator, or another piece of technology, to find the zeros of the function f(x)=−2x^3+5x^2+1

What are the approximate zeros to the nearest tenth?

There may be more than one correct answer. Select all correct answers.

• x≈0.2
• x≈−0.2
• x≈1.7
• x≈−2.58
• x≈−1.7
• x≈2.58