Sunday
May 24, 2015

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

Calculus
A box with a square base and no top is to have a volume of 32 ft3. What dimensions use the least amount of material (in other words what dimensions give minimum outside surface area)?
Sunday, May 24, 2015 at 6:54pm

Calculus math
how do i solve these quadratics? c=10000 9a+3b+c=7975 36a+6b+c=6400 im unsure of how to solve as a and b are unknowns...
Thursday, May 21, 2015 at 11:20pm

Calculus
Which of the following functions is continuous at x = 5? I put a for my answer, could someone please check this? a. f(x)=(x^2-25)/(x+5) b. (x^2-25)/(x-5), x cannot equal 5 20 when x equals 5 c.(x^2-25)/(x-5), x cannot equal 5 0 when x equals 5 d. all of the functions are ...
Thursday, May 21, 2015 at 9:51pm

calculus
Peter the punter decided to place $10,000 into a high growth share portfolio. After 3 weeks his investment was looking rather sad, with the value of his portfolio falling $2,025. Unperturbed, Peter stuck with his original plan to hold the stock for at least 6 months. But after...
Thursday, May 21, 2015 at 6:24am

Calculus and quadratic equations
Peter the punter decided to place $10,000 into a high growth share portfolio. After 3 weeks his investment was looking rather sad, with the value of his portfolio falling $2,025. Unperturbed, Peter stuck with his original plan to hold the stock for at least 6 months. But after...
Wednesday, May 20, 2015 at 11:50pm

Calculus
Which of the following statements is/are true? I.If f '(c) = 0, then f has a local maximum or minimum at x = c. II.If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b]. III.The Mean Value Theorem can be ...
Wednesday, May 20, 2015 at 9:19pm

Calculus
The function's value will always be greater than or equal to the local linear approximation of a function f if, for all x in an interval containing the point of tangency, f " > 0 f " < 0 f ' > 0 f ' < 0
Wednesday, May 20, 2015 at 9:17pm

Calculus
The function's value will always be greater than or equal to the local linear approximation of a function f if, for all x in an interval containing the point of tangency, f " > 0 f " < 0 f ' > 0 f ' < 0
Wednesday, May 20, 2015 at 9:17pm

Calculus
(a) Consider the region in the xy-plane consisting of the points (x; y) satisfying x > 0, y > 0, and lying between the curves y = x^2 + 1, y = 2x^2 2 and the two axes. Draw a diagram of this region. (b) This region is rotated about the y-axis to form a solid glass vase. ...
Tuesday, May 19, 2015 at 10:21am

Calculus
If the integral from 0 to 8 of f(x)=4, then calculate the integral of f(4x) from 0 to 2.
Tuesday, May 19, 2015 at 8:31am

Calculus
Let f : R --> R be an odd function. Explain why, for any positive number a, the integral from -a to a of f(x) = 0.
Tuesday, May 19, 2015 at 8:10am

Calculus
The following definite integral gives the area of the region between the graph of the function f(x) = Icosx - x^2I (I=modulus), the x-asis, and the lines x=-2 and x=2. the integral of mod cosx - x^2 from -2 to 2. Describe a different region whose area is given by this integral...
Tuesday, May 19, 2015 at 5:56am

Calculus
Let f for all Real numbers, be an odd function. Explain why, for any positive number a, the integral from -a to a of f(x) = 0.
Tuesday, May 19, 2015 at 5:28am

Quadratic Functions and Calculus
Peter the punter decided to place $10,000 into a high growth share portfolio. After 3 weeks his investment was looking rather sad, with the value of his portfolio falling $2,025. Unperturbed, Peter stuck with his original plan to hold the stock for at least 6 months. But after...
Tuesday, May 19, 2015 at 2:49am

Calculus
Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x^(1/3) + 6x^(4/3). You must justify your answer using an analysis of f '(x) and f "(x). I found the first and second derivative which i think is (8x+1)/(x^(2/3), and the ...
Monday, May 18, 2015 at 7:09pm

Calculus
The position function of a particle in rectilinear motion is given by s(t) s(t) = t^3 - 9t^2 + 24t + 1 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.
Monday, May 18, 2015 at 6:09pm

Calculus
Please check my answers. Solve the following equations and/or system of equations for the unknown variables. 1. x^2-3x-12=0 x= 3 + sqrt(57) / 2, x= 3 - sqrt(57) / 2 2. x+y=8 , 3x+2y=2 x=-14, y=22 3. 3x + 2y =10 , x+y=5 , y+z =9 x=0,y=5, z=4 4. 1/x-p1z=0, 1-p2z=0, I-p1x-p2y=0 ...
Monday, May 18, 2015 at 9:28am

Calculus
Given h(x)=(6x^2+x)/x , find h'(0)
Monday, May 18, 2015 at 12:31am

Calculus
If f(5) = 7, then lim f(x) ------------------x-> 5
Monday, May 18, 2015 at 12:06am

Calculus
If f(5) = 7, then lim f(x) x-> 5
Monday, May 18, 2015 at 12:05am

Calculus
I really need help with this calculus question. I ve been struggling to figure it out. Imagine making a tent in the shape of a right prism whose cross section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.6m^3, to ...
Sunday, May 17, 2015 at 4:15pm

Calculus 2
How would you find the following. A step by step process would greatly be appreciated. 1) Convert the polar equation to a rectangular equation. r^2 = 8sin2θ
Sunday, May 17, 2015 at 2:46pm

calculus
velocity of a particle- the displacement s (in meters) of a particle moving in a straight line is given by the equation of motion s=4t^3+6t+2, where t is measured in seconds. Find the velocity of the particle s at times t=a t=1 t=2 t=3
Saturday, May 16, 2015 at 7:13pm

calculus
velocity of a ball- if a ball is thrown into the air with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y=40t-16t^2. find the velocity when t=2
Saturday, May 16, 2015 at 7:11pm

calculus
find the derivative of the function at the given number F(x)= 1/ √x at 4
Saturday, May 16, 2015 at 7:09pm

calculus
find an equation of the tangent line to the curve at the given point. graph the curve and the tangent line y=x/x-1 at (2,2) )
Saturday, May 16, 2015 at 4:39pm

Calculus
Solve the following differential equation with initial conditions: y"=e^(-2t) + 10^(4t); y(0)=1, y'(0) = 0
Friday, May 15, 2015 at 4:26pm

Calculus
Suppose a certain country's population has constant relative birth and death rates of 97 births per thousand people per year and 47 deaths per thousand people per year respectively. Assume also that approximately 30000 people emigrate (leave) from the country every year. ...
Friday, May 15, 2015 at 4:07pm

Calculus
The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours. (10 points) a. Estimate the value of T'(6). Give units in your answer. b. What is the meaning of T'(6)? t ...
Friday, May 15, 2015 at 2:21pm

Calculus
The slope of the line normal to the curve e^x − x^3 + y^2 =10 at the point (0, 3) is ____
Thursday, May 14, 2015 at 7:56pm

Calculus
Center at (2,-5), conjugate axis parallel to the y-axis, slopes at assymptotes numerically one-sixteenth times the length of the latus rectum, and distance between foci is 2 sqr t145.
Thursday, May 14, 2015 at 2:29pm

Calculus, Riemann Sums
Measurements of a lake’s width were taken at 15-foot intervals, as shown: x= 0 15 30 45 60 75 90 105 120 f(x)= 0 15 18 20 19 23 24 22 12 Estimate integral (0,120) f(x) dx with n = 4, using Midpoint approximation. For this question, I ended up with 7200 but compared to the...
Tuesday, May 12, 2015 at 11:57am

Calculus
Problem: Find the general solution to the following differential equation: x y' +x = ycos(1/x) I assume that you do separation of variables here: x(dy/dx) +x = ycos(1/x) xdy+x = (ycos(1/x)) dx ....? I'm stuck on how to simplify this. Thank you!
Tuesday, May 12, 2015 at 12:48am

Pre-Calculus (absolute values)
I want to find the invariant points( points that are fixed) algrebraically of x^2 - 25 and its reciprocal. Would I set up my equation like this? 0 = x^2 -25 or 0 = 1/ x^2 - 25 Thanks
Tuesday, May 12, 2015 at 12:43am

Calculus
f(x)=xe^-x^2. What interval is this function increasing.
Monday, May 11, 2015 at 11:54am

pre calculus
Given that sinx= 3/5 and that x terminates in Quadrant 2 , determine the values for cosx and tanx Find Cos x/2
Monday, May 11, 2015 at 10:43am

Pre-calculus ( Absolute value)
Why does |7 + 3x| = x -1 have no solution? I could plug in, for example 5, and the answer would be positive. Thank you =)
Sunday, May 10, 2015 at 10:15pm

Pre-Calculus
Can someone please explain on how to solve this equation so I can do the others that are similar to this one? Find the solutions of the equations that are in the interval [0,2pi) cos x cot^2 x= cos x Thank you!
Saturday, May 9, 2015 at 11:19pm

Calculus
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical value, state whether the ...
Friday, May 8, 2015 at 10:07pm

calculus
Integral of 1/[x^2(1+x^2)]
Friday, May 8, 2015 at 7:34pm

calculus(urgent pls)
Integral of 1/[x^2(1+x^2)]
Friday, May 8, 2015 at 5:52pm

Calculus, derivatives
The curve is given by x^2+2r(sqrt(y))=xy What is dx/dr when y is constant?
Friday, May 8, 2015 at 4:08pm

Calculus(URGENT PLS!!!)
Find the integral of (e^cosx)sinx
Friday, May 8, 2015 at 2:48pm

Calculus
Find the area of the region bounded by f(x)=5xsqrt(121−x2) and the x-axis. The area is = to
Friday, May 8, 2015 at 2:33pm

Calculus - Derivative
The curve is given by x^2+2r(sqrt(y))=xy What is dx/dy when r is constant?
Friday, May 8, 2015 at 1:34pm

Calculus
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency f '(x) < 0 f '(x) > 0 f "(x) < 0 f "(x) > 0
Thursday, May 7, 2015 at 10:40pm

Calculus
The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals of (0.12,1), if any, is the graph...
Thursday, May 7, 2015 at 9:10pm

Calculus
Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither ...
Thursday, May 7, 2015 at 9:03pm

Calculus
If f is a function such that [(f(b)-f(a))/(b-a)]=2 , then which of the following statements must be true? a.f(a) = f(b) = 2 b.The slope of the tangent line to the function at x = a is 2. c.The average rate of change of the function on the interval [a, b] is 2 d.The linear ...
Thursday, May 7, 2015 at 3:28pm

Calculus
True or False If f is continuous at x = c, then f is differentiable at x = c.
Thursday, May 7, 2015 at 3:22pm

Calculus
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency f '(x) < 0 f '(x) > 0 f "(x) < 0 f "(x) > 0
Thursday, May 7, 2015 at 3:20pm

Calculus
Find the average value of the function f(x)= 8/ (3+x)^2 on the interval [0,2]
Thursday, May 7, 2015 at 7:32am

Calculus
A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
Thursday, May 7, 2015 at 7:28am

Calculus
The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
Thursday, May 7, 2015 at 7:27am

Calculus
Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
Thursday, May 7, 2015 at 7:23am

Calculus
Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
Thursday, May 7, 2015 at 7:22am

calculus 1 (I need help)
The portion of the ellipse x^2/9+y^2/4=1 with x greater than or equals to 0 is rotated about the y-axis to form a solid S. A hole of radius 1 is drilled through the center of S, along the y-axis. Find the exact volume of the part of S that remains. Show all steps. (Hint: use ...
Wednesday, May 6, 2015 at 8:43pm

calculus
Use table of integrals to evaluate the integral of x^4 sinxdx.
Wednesday, May 6, 2015 at 8:38pm

Calculus
Find the average value of the function f(x)= 8/ (3+x)^2 on the interval [0,2]
Wednesday, May 6, 2015 at 8:33pm

Calculus
A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
Wednesday, May 6, 2015 at 8:31pm

Calculus
The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
Wednesday, May 6, 2015 at 8:30pm

Calculus
Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1
Wednesday, May 6, 2015 at 8:27pm

Calculus
Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.
Wednesday, May 6, 2015 at 8:23pm

Calculus
Find the area of the region bounded by the curves y=x^2 - 2x and y= x + 4
Wednesday, May 6, 2015 at 8:22pm

Pre-Calculus
Evaluate. 1-|200+||-2|(-5)^3|| I get 49 as an answer
Wednesday, May 6, 2015 at 8:05pm

calculus
find the exact arc length of the curve: y=0.5(e^x + e^-x) for 0 is less than or equal to x and x is less than or equals to ln2.
Wednesday, May 6, 2015 at 6:11pm

Calculus
What is the derivative of tan(1-x)^(1/2)?
Wednesday, May 6, 2015 at 5:13pm

Calculus
The graph of f '(x) is continuous and decreasing with an x-intercept at x = -3. Which of the following statements must be true?
Monday, May 4, 2015 at 5:46pm

Calculus max/min
d=0.767. There are two parallel sidewalks that are separated by the park that is 600 feet wide. You are standing on the south sidewalk facing east. On the north sidewalk, 2000 feet ahead of you, is a bus stop. You can walk on the sidewalk at 5.5+d feet per sec. You can walk ...
Sunday, May 3, 2015 at 10:44pm

Calculus 2
Find the radius of convergence and interval of convergence of the series. There is an infinity sign on top of the summation symbol and "n=1" underneath it. To the right of the summation symbol is x^n/5n! How would you find the radius of convergence and interval of ...
Sunday, May 3, 2015 at 7:04pm

Calculus
A wedge is cut from a right circular cylinder of radius r by two planes, one perpendicular to the axis of the cylinder and the other making an angle (beta) with the first. Find the volume of the wedge by slicing perpendicular to the y-axis. Please show all steps
Sunday, May 3, 2015 at 7:00pm

calculus
h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. What values of a make h(x) strictly decreasing? I know h'(x) has to be less than zero for h(x) to be decreasing and h'(x) = 1-asin(ax). I'm not sure where to go from here...
Saturday, May 2, 2015 at 3:40pm

Optimization Calculus
A three sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. There is 96 ft of fencing available. Find the maximum enclosed area and the dimensions of the corresponding enclosure. I drew a picture of it and I got ...
Saturday, May 2, 2015 at 3:02pm

Calculus
h(x) = x+cos(ax) is a family of functions where a is a positive constant such that 0<a<4. Which values of a make h(x) strictly decreasing? Justify your answer. I can't figure this out and help would be appreciated. Thanks in advance!
Saturday, May 2, 2015 at 12:43pm

Calculus
h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 + ...
Friday, May 1, 2015 at 2:19pm

Calculus
h(x)= x + cos(ax), where a is a positive constant such that 0 < a < 4. For what values of a will h(x) have a relative maximum at x=1? So I found the derivative and got h'(x) = 1- asin(ax). Then I plugged in 1 for x and set the derivative equal to zero, so I have 1 - ...
Friday, May 1, 2015 at 2:16pm

Calculus
Imagine making a tent in the shape of a right prism whose cross-section is an equilateral triangle (the door is on one of the triangular ends). Assume we want the volume to be 2.2 m3, to sleep two or three people. The floor of the tent is cheaper material than the rest: assume...
Thursday, April 30, 2015 at 11:44pm

Calculus
What is the solution to the following system of equations -2x+3y+z=5 x+5y+2z=17 To do this, I used elementary operations and isolated x to get 13y+5z=37. Is that correct so far? How would I continue?
Thursday, April 30, 2015 at 3:32pm

Calculus
How would I find the equilibrant of three vectors? I am given a graph of three different vectors which meet at the point (0,0)
Thursday, April 30, 2015 at 2:04pm

Calculus
If 3(a,3,2)-2(3,b,b)=(-3,1,-2) determine a and b. Describe the set spanned by the vectors. I don't know how to answer this
Thursday, April 30, 2015 at 1:40pm

Calculus
I'm not sure how to do this; I figured I should use separation of variables but I got the wrong equation. Help is appreciated, thanks! If dy/dx=(1+x)/(xy), x > 0, and y = –4 when x =1, when x =3, y = ? A. 6.433, −6.233 B. 3.898, −3.898 C. 4.711, −...
Thursday, April 30, 2015 at 12:19pm

Calculus
What are the coordinates of the point on the graph of f(x)=(x+1)(x+2) at which the tangent is parallel to the line with equation 3x-y-1=0? a)(-3,2) b)(-1,0) c)(0,2) d)(1,6) To answer this, I put f(x)=(x+1)(x+2) into the form f(x)=x^2+3x+2 and found the derivative which is f&#...
Thursday, April 30, 2015 at 10:21am

Calculus and Vectors
A plane is flying south east at a constant speed of 900km/h. The wind is blowing towards the north at 100km/h. Determine the resultant velocity of the plane relative to the ground.
Wednesday, April 29, 2015 at 5:24pm

Calculus
What does it mean to span in R2? I have this question: Which of the following sets if vectors span R2? a) {(1,1),(-2,-2)} b) {(1,1),(1,2)} c) {(1,2),(1/2,2)} d) {(-1,1),(1,-1)}
Wednesday, April 29, 2015 at 5:22pm

Calculus
An airplane is heading due east with an airspeed of 220km/h when it encounters a wind from the south at 76km/h. What is the direction of the resultant velocity of the airplane The answer is E19.06°N but I don't know how
Wednesday, April 29, 2015 at 4:49pm

calculus
Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4."
Wednesday, April 29, 2015 at 3:24pm

Calculus-limits
What is the limit as x approaches a of (sinx-sin a)/(x-a)? a. -sin a b. cos a c. -sin x d. cos x e. undefined Thanks!
Wednesday, April 29, 2015 at 1:56pm

calculus
For the function f(x)=x^3e^x, determine intervals of increase and decrease and the absolute minimum value of f(x) To do this I found the derivative which is f'(x)=3x^2e^x. Then I set it to zero: f'(x)=0 0=3x^2e^x How would I isolate x? And when I do, I would sub that x...
Wednesday, April 29, 2015 at 1:52pm

Calculus-limits
I'm studying for the AP exam and I can't figure this problem out. I thought the answer was negative infinity but that isn't an option. Thank you in advance! What is the limit as x approaches infinity of (9x-x^2-7x^4)/(x^3+12x)? a. 9 b. 7 c. -7/12 d. -7 e. Does not ...
Wednesday, April 29, 2015 at 1:32pm

Calculus
Can you please explain how I would solve these questions? 1) Which point is 2 units from the line 12x-9y-5=0? a)(8,3) b)(7/6, -7/3) c)(14,6) d)(1,1) 2.) Which of the following sets of vectors spans R2: a) {(1,1),(-2,-2)} b) {(1,1),(1,2)} c) {(1,2),(1/2,2)} d) {(-1,1),(1,-1)}
Wednesday, April 29, 2015 at 12:16pm

calculus
1.Solve the differential equation dy/dx= y^2/x^3 for y=f(x) with the condition y(1) = 1. 2.Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared. Explain why the initial value problem y prime equals the ...
Tuesday, April 28, 2015 at 10:54pm

Pre-Calculus
Explain the difference between sin^-1(x) and 1/sin(x), Are there different expressions for both these functions?
Tuesday, April 28, 2015 at 9:30pm

Pre-Calculus
At 34 degrees north latitude, the longest day of the year has 14.273 hours of daylight, and the shortest day 9.726 hours. If the equinox falls on march 21(day 80), model the hours of the daylight by day?
Tuesday, April 28, 2015 at 9:29pm

Pre-Calculus
f(x) is a sinusoidal curve with maximum at f(0)=10 and next minimum at f(6)=0. Find the equation?
Tuesday, April 28, 2015 at 9:28pm

Calculus
Piecewise function problem. Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x<1. If the function is differentiable, find the sum of a+b.
Tuesday, April 28, 2015 at 9:26pm

Calculus
The rate of change of atmospheric pressure P with respect to the altitude h is proportional to P provided that the temperature is consistent. At 15 degrees Celsius, the pressure is 101.3 pounds per square inch (psi) at sea level and 87.1 psi at height 1000m. Find the pressure ...
Tuesday, April 28, 2015 at 9:13pm

Calculus
Susan pulls on a rope sleigh with a force of 120 N. If the rope makes an angle of 25 degrees with the horizontal, what is the force that tends to lift the sleigh? a)120.00 N b)108.76 N c)50.71 N d)84.85 N how would you know?
Tuesday, April 28, 2015 at 8:39pm

Calculus
Can someone check my work on this problem? I'm studying for the AP test and I would really appreciate any help. Let f(x) = the definite integral from [-2,(x^2-3x)] of e^(t^2) dt At what value of x is f(x) a minimum? a. For no value of x b. 1/2 c. 3/2 d. 2 e. 3 The answer I...
Tuesday, April 28, 2015 at 4:26pm

Calculus
Find the area of the largest rectangle that fits inside a semicircle of radius 10 (one side of the rectangle is along the diameter of the semicircle).
Tuesday, April 28, 2015 at 2:25pm

Calculus help??
I'm not sure how to solve this and help would be great! d/dx [definite integral from 0 to x of (2pi*u) du] is: a. 0 b. 1/2pi sin x c. sin(2pi x) d. cos (2pi x) e. 2pi cos (2pi x) This is the fundamental theorem, right? What's confusing me is the u and du and the end. ...
Tuesday, April 28, 2015 at 2:12pm

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