I Need Help With These Calculus Questions

How to start these calculus questions?

You're on the right track with "arctan" but let's go back one step. Try the substitution x = tan(u). Why? Because then
1 + x^2 = 1 + tan^2(u) = sec^2(u)
and also dx/du = sec^2(u) so that the sec^2(u) cancel each other out! When x=1, u=arctan(1) = pi/4 and when x=sqrt(10), u = arctan(sqrt(10))
In other words, the definite integral
4 int_{x=1}^{x=sqrt(10)} dx/(1+x^2)
becomes in terms of u
4 int_{u=pi/4}^{u=arctan(sqrt(10))} du
=4[arctan(sqrt(10)) - pi/4].

For the first one, you need to split the range of integration up from x=-1 to 1 with integrand f(x)= x and then from x=1 to x=7 with f(x)=1/x.

Need help in Two calculus questions?

Question 1:

You know that the slope of the given line is -1/2. The slope of a line tangent to the curve is given by the derivative, which is f'(x) = -2/(x - 1)^2.

Now, set these slopes equal to each other and solve for x, which yields two values: -1 and 3. These are the x-values for the points on the curve through which the tangent lines pass.

Finding f(-1) and f(3) will give you the ordered pairs on the curve: (-1, 0) and (3, 2). So we know that one line tangent to the curve with slope 6 contains the point (-1,0) and the other line contains the point (3, 2).

Finally, using these two points and a slope of -1/2, find the equations of the tangent lines:

y = -(1/2)x - 1/2 and y = -(1/2)x + 7/2


Question 2:

s(t) is the height at time t. The velocity is given by the derivative of s.

So, v(t) = s'(t) = -32t - 28

To find the velocity after falling 228 feet, you must first find t using s(t):

241 = -16t^2 - 28t + 241 (BE CAREFUL: height is 469 - 228)
t = 3 seconds

Now find v(3) = -32(3) - 28 = -124 ft/s

I need help with these math questions.?

1) 4(4+5)divided by 3(10-7)
P: so the 4+5 and 10-7 since theyre in paranthesis
so you now have 4(9) divided by 3(3)

E: none

M: would be 4(9) which is 36 and 3(3) which is 9

D: so you now have 36 divided by 9
which is 3

A: none

S: none

2) 2(105 divided by 15 - 6)
P: 105 divided by 15 - 6

E. none

M: 2(whatever the answer in the parathesis is)

D: 105 divided by 15 which is 7
so its now 7-6 in the paranthesis

A: none

S: 7-6 is 1
now you have 2(1) which is 2

3) (2 x 11 +1) - (3 x 6 + 5)
P: you can see whats in the paranthesis

E: none

M: 2x11 is 22 so now that one is (22+1) then the next multiplacation is 3x6 in the other paranthesis which is 18 so now that one is 18 + 5

D: none

A: (22+1)= 23 then the other is 18+5 which is 23

S 23-23 is 0

there you go..hope i taught well enough O.o

I need help with these math questions.?

John, Robert, Dominique, Clarice, and Marco work for a small publishing company. The Company is going to send 2 of these employees to a statistics conference in California.
- How many possible combinations are possible if two workers are selected at random?
- What is the probability that Clarice will be selected?
- What is the probability that John will not go to the conference?
According to a recent survey, 25 percent of US households are wireless, have no landlines for telephones. In a random sampling of 20 households, what is the probability that:
- Exactly 5 are wireless?
- Fewer than 3 are wireless only?
- At least 3 are wireless only?
- The number of households that are wireless-only is between 5 & 7, inclusive?
An allergy, education is developed to combat a number of allergies. In a clinical test, 5 percent of the patients in the study experienced insomnia as a side effect. A random sample of 20 users is obtained. From this sample, determine:
- The probability that exactly 3 will experience insomnia.
- The probability that 3 or fewer experienced insomnia.
- The probability that between 1 & 4 patients, inclusive experienced insomnia.
- If it would be unusual to find 4 or more patients who experienced insomnia. Why?
- If 240 of the users are randomly selected, how many would be expected to experience insomnia?
- Would it be unusual to observe 20 patients with insomnia form these 240 individuals?

I Need help with these Math Question?

PETTI MICRO FINANCE INT. (LOAN OFFER AT 5% INTEREST RATE) We offer Loans to individuals, Firms and cooperate bodies at 5% interest rate per annual, The Minimum amount you can borrow is $2,000.00 US Dollars to Maximum of $10.Million. Please, provide the following:
1. Name Of Applicant:.......
2. Age:......................
3. Location:.................
4. Amount Needed........
5. Duration:.................
6. Phone Number.............
7. Fax Number...............
8. Address...............
9. Occupation:...............
10.Country:....................
11.State:...........................
12.City:...........................
13.Post Code:.........................
14.Monthly Payment:
You can contact me today if you are interested in getting a loan in
this company, contact me for more information about the loan process,
process like the loan terms and conditions and how the loan will be
transferred to you. I need your urgent response if you are
interested.
Contact Email:Email:frank_petti58@yahoo.com
Sincerely,
Mr.Petti,

I need help on these calculus problem?

1) y = x/(1 + x^2)
Differentiating,
y' = (1+x^2)*1 - x(0+2x)/(1+x^2)^2
y' = (1+x^2-2x^2)/(1+x^2)^2
y' = (1-x^2)/(1+x^2)^2
The tangent passes through (2, 0.4)
Putting x=2,
y' = (1-2^2)/(1+2^2)^2 = (1-4)/(1+4)^2 = -3/25
Equation of the tangent:
y - 0.4 = y'(x - 2)
y - 0.4 = (-3/25)(x-2)
Multiplying by 25,
25y - 10 = -3(x-2)
25y - 10 = -3x + 6
3x + 25y - 16 = 0
Ans: 3x + 25y - 16 = 0

2) Use the equations and relations given below to answer the following questions.
f(pi/3) = 6, f ' (pi/3) = -10
g(x) = f(x) sin(x), h(x) = (cos(x))/(f(x))
find g' (pi/3) and h' (pi/3) =2

3. Suppose that f(1) = -1, f '(1) = -2, g(1) = 3, and g'(1) = 3. Find the following values.
(a) (fg)'(1)
(b) (f/g)'(1)
(c) (g/f)'(1)

4. y = sin(4x)
Substitute 4x=u:
y = f(u) = sin(u)
Ans: sin(u)

5. y=sqrt(8 +3 x)
Substitute 8+3x=u:
y = f(u) = sqrt(u)
Ans: sqrt(u)

6. y=tan(cos(x))
Substitute cos(x) = u:
y = f(u) = tan(u)
Ans: tan(u)

7. If F(x) = f(g(x))
Differentiating by chain rule,
F'(x) = f'(g(x)) * g'(x)
Substituting x = -5
F'(-5) = f'(g(-5)) * g'(-5)
Substituting g(-5) = 2, g'(-5) = 3,
F'(-5) = f'(2) * 3
Substituting f'(2) = 6,
F'(-5) = 6 * 3 = 18
Ans: 18

8. 1st derivative = -sin(3x)(3)
2nd derivative = -cos(3x)(3^2)
3rd derivative = sin(3x)(3^3)
4th derivative = cos(3x)(3^4)
We have to find 60th derivative. 60 is a multiple of 4.
Therefore 60th derivative = cos(3x)(3^60)
Or 3^60 * cos(3x)
Ans: 3^60 * cos(3x)

9. y=abs(x)/sqrt(5-x^2)
Around point (2,2), abs(x) = x
y = x/sqrt(5-x^2)
Take square of both sides.
y^2 = x^2/(5 - x^2)
Differentiating,
2yy' = [(5-x^2)(2x) - (x^2)(-2x)]/(5-x^2)^2
2yy' = (10x-2x^3+2x^3)/(5-x^2)^2
2yy' = (10x)/(5-x^2)^2
Substituting (x,y) = (2,2)
2*2*y' = (10*2)/(5-2^2)^2
4y' = 20/1 = 20
y' = 20/4 = 5
Equation of line with slope 5 and passing through (2,2):
y - 2 = 5(x-2)
y - 2 = 5x - 10
5x - 10 - y + 2 = 0
5x - y - 8 = 0
Ans: 5x - y - 8 = 0

I need help with these math questions?

If a square shelf's area is 500 square inches, each side of the shelf must be between -
22 in and 23 in


6.Which of the following is correct?

B. 0.115 < 1/5

4.Oranges are priced at about 88 cents. About how much would you pay for 10 oranges? Not here


5. Lena invited 3 girls and 4 boys to a party. She expects each boy to drink at least 4 cans of soft drinks and each girl to drink no more than 2 cans of soft drinks. Soft drinks come in cartons of 6 cans. What is a reasonable number of cartons of soft drinks for Lena to buy?
C. 3 to 4 cartons

3. Denise corectly answered 26 questions on a 30 - question reading test. Which expression could be used to find the percent of questions Denise did NOT answer corectly?
B. 26/ 30 * 100

1. A store manager displayed 500 candy bars on a shelf. On the following Friday,onyly 25 candy bars remained on the shelf. Which expression could be used to find the percent of candy bars that were sold?
C. 475/500 * 100

4. Victor made porsters for a talent show. If he could print 7 posters every 15 1/4 minutes on the copy machine, how long did it take Victor to print 21 posters
B. 45 3/4

5. Glen correctly answered 35 of te 42 problems on his math test. Which expression could be used to find the percent of the problems he answered correctly
B. 35/42 * 100

5. A survey shows that 2/3 of the student body perfers apple juice to oange juice. If 2,574 students took part in the survey, how many students do NOT prefer apple juice?

A. 858

2. Lake Henry held 17,857 fish. The park service relocated 4/7 of the fish to populate a new lake. How many fish remained in Lake Henry?
7653

5. At Marshall Middle School, 16 of the school's 640 students are student council officers. What percent of the students at the school were student council officers?
D. 2.5%

I REALLY NEED HELP WITH THESE MATH QUESTIONS.?

1. Principal, $900.00; rate, 10%; time, 3 years

a. $90.00
b. $27,000.00
c. $9,000.00
d. $270.00

Interest = Principal * rate * time. Let's start by using the process of elimination. Answer a is wrong because it is 10% of the principal, but the money was invested for three years, not one. Answers b and c are wrong because they are greater than the principal, and the rate is less than 100%. That leaves answer d. Let's check with the equation
I = P * R * T
I = $900 * 10% * 3 = $900 * .1 * 3 = $270.

Problems 2-4 are solved in the same way. For problems 5-8, figure out the interest and add it to the principal to find the answer (in the case above, you would add the $270 to the $900 and your answer would be $1,170

The rest are solved in the same manner of these first two groups. If you cannot figure it out from there, you need in-person help OR you need to flunk the course and take it over so you can understand.

Calculus antiderivatives; i need help!?

I need help to understand the answers to these questions and how to arrive at them
1. Find f.
f ''(x) = 60x2 + 6x + 2
f(1) = 1
f '(1) = -4
2.Find the most general f. Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.
f '' (x) = 3 + x3 + x8
3. Find the antiderivative of...
a. f(x) = (x + 2)(2x + 3)
b.http://www.webassign.net/www28/symImages/a/a/8e2f560ee5a09238f9529feb2382fd.gif
c.http://www.webassign.net/www28/symImages/f/1/d087edd61f4266522501bb33f2b18b.gif
d.http://www.webassign.net/www28/symImages/9/c/85124fb3cea799898bfe822efd6e6a.gif
4.Find f.
f ''(t) = 3/√t
f(4) = 22
f '(4) = 5