# Calculus

**Calculus**

A box (with no lid) is to be constructed from a sheet of card board by cutting the squares from corners and folding up the sides. Suppose the original sheet of card board measures 16 inches by 16 inches. What would the size of the squares removed to maximize the volume of the ...

**calculus**

Find the volume generated by revolving about the x-axis the region bounded by the following curves y=sqrt/(4x+3),x=0,x=4, and y=0. (Use "pi" for π).

**Differential Calculus**

A norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window 10 m, express the area A of the window as the function of width x of the window.

**Calculus**

Use implicit differentiation to find the derivative of y with reapect to x x^2y-y^2+ln(xy)=1

**Calculus - Discontinuity**

What kind of discontinuity is this piecewise function? Removable or jump? f(x) ={ (2x^2 - 5x - 3)/(x-3) if x does not equal 3 ............6............................if x = 3

**Calculus**

What kind of discontinuity is this: F(x)= (2x^2 - 5x -3)/(x-3) if x does not equal 3 6 if x=3 It is a pieces use function. I thought it was removable but my answer key says it is a jump discontinuity. This is from an exam review and I want to get it right.

**calculus**

Find the general solution of the equation. 6t*dy/dt+y=sqrt (t),t>0.

**calculus**

500-gallon tank initially contains 200 gallons of brine containing 100 pounds of dissolved salt. Brine containing 2 pounds of salt per gallon flows into the tank at the rate of 4 gallons per minute, and the well-stirred mixture flows out of the tank at the rate of 1 gallon per...

**calculus**

Given a closed box with surface area = 16 and a square bottom, what value of x will maximize the volume of the box?

**calculus**

What function should be used to minimize the distance between and the point (2, 0)?

**calculus**

Given the area of a rectangle is A = bh, and assuming the rectangle is open on one side, perimeter b + 2h = 40, what formula will maximize the area of the rectangle

**calculus**

a particle is moving along the curve whose equation is" y=x^2? At what point on the curve are the x and y coordinates changing at the opposite rate?

**Calculus**

The base of a solid is the region bounded by the lines y = 5x, y = 10, and x = 0. Answer the following. a) Find the volume if the solid has cross sections perpendicular to the y-axis that are semicircles. b) Find the volume if the solid has cross sections perpendicular to the ...

**General Physics**

Clarification: this is calculus-based physics, so the methodology is not restricted to trigonometry only. I have two questions, so hopefully I can divide them up nice and evenly. Also, if you know where I should copy and paste proper vector notation from, please tell me so I ...

**Calculus**

Related rates: The volume of a cube is increasing at the rate of 40 mm^3/s. How fast is the surface area of the cube increasing when each edge is 10 mm?

**CALCULUS**

State the intercepts, domain and range for y= |0.5x^2-2|.

**CALCULUS**

Let y(t) denote the mass of a radioactive substance at time t.t. Suppose this substance obeys the equation y′(t)=−14y(t). Assume that, initially, the mass of the substance is y(0)=M>0. At what time does half of the mass remain? (Round your answer to 3 decimal ...

**Calculus**

A tetrahedron is formed in the rst quadrant by the three coordinate planes and the plane that meets the x-axis at a > 0, the y-axis at b > 0 and the z-axis at c > 0. Compute its volume. Kindly help

**Calculus**

The position, p(t), of an object at time t is given. Find the instantaneous velocity at the indicated time c. Also determine whether it is moving forward, backward, or neither at time c. p(t)=2-1/t at c=3

**Calculus**

Find the area under the curve of y=-2x+6 from x=0 to x=3 using 3 strips of equal length using right endpoints. I tried this equation before and my answer was 9 but my teacher said it was wrong? and I also posted this before and Someone who helped me got the same answer. So I'm...

**Calculus**

Given the function 6x+3y=18, find the area under the curve from x=0 to x=3 using 3 strips of equal length using the right end points. I was working on this and so I made the equation equal to Y=mx+b form so it ends up being Y=-2x+6, and now I am completely confused.. Please ...

**Calculus**

lim x-->0 ((7-3x^5+x^2sinx)/(5cosx))

**calculus**

find the constants a and b so the function is continuous on a real line piecewise function: f(x)={5, if x<= -2; ax+b, if -2<x<3; -5, if x>=3 I know the limit x-->2- is 5 and limit x-->3+ is -5. I don't know how to find the constants

**CALCULUS**

∫4x^−1*sin(ln(6x))dx I got 4*[-cos(ln(6x))]+C but its wrong and im not sure why... Please Help!! Thanks

**Calculus**

find the value of a, if it exists, such that the following function is continuous at X = 2. piecewise function f(x)={x^2-3x+1, if x>2; a, if x=2; 3-2x, if x<2 I found the limits from left and right of 2 = -1 so the limit exists but I don't know how to figure out a

**Calculus**

F(x)=2x^2-log(x+5)/√16+x

**CALCULUS**

Find the derivative of y=4sinx−2cosx

**calculus**

A rectangular lot is to have an area of 1600m^2. Find the shortest that can can reach the building with one end resting on the ground outside the wall

**Calculus**

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given points. x 4 9 11 14 15 f(x) -6 -11 -18 -21 -25 -11...

**Calculus- PLEASE HELP**

A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the original dimensions of the rectangular piece ...

**Calculus**

A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the original dimensions of the rectangular piece ...

**Calculus- Reiny**

Thanks for the help, but do you understand what Im suppoosed to graph on 2D d) Use a graphing calculator to sketch the graph of y = V(x). Use the viewing window [0, 24, 4] by [-2500, 4000, 500]. Then use the 2 nd – TRACE – maximum feature to calculate its maximum point. ...

**Calculus**

A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the original dimensions of the rectangular piece ...

**Calculus**

let f(x)=2x-7. Use the rigorous definition of limit to show that lim x-->4 f(x)=1

**AP Calculus AB**

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given points. x 4 9 11 14 15 f(x) -6 -11 -18 -21 -25 -11...

**Calculus**

lim x--> 2+ (tan(pi/x))

**Calculus**

Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.

**Calculus**

Use pinching theorem to evaluate lim x-->1 ((x-1)sin(1/x-1)) I'm confused in the pinch theorem analytically

**Pre-Calculus**

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and...

**Pre-Calculus Matrix**

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 4 -1 3 12 1 4 6 -32 5 3 9 20 I believe that the solution does not exist and how can I prove that?

**Pre-Calculus**

Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 I really need help.. 1 1 1 -5 1 -1 3 -1 4 1 1 1 -2 I've done so many different methods to solve this and I get stuck..

**Pre-Calculus**

The Fiedler family has up to $130,000 to invest. They decide that they want to have at least $40,000 invested in stable bonds yielding 5.5% and that no more than $60,000 should be invested in more volatile bonds yielding 11%. How much should they invest in each type of bond to...

**pre-calculus**

A plane flies at a speed of 150mph at an angle of 10 degrees, after 6 seconds, the plane keeps the same speed but changes to an angle 18 degrees. How long in minutes would it take the plane to travel to a cruising altitude of 30,000 feet?

**maths-calculus help me**

differentiate Arccosh(x^2+1)*dy/dx if y=arcsinh(coth(x^2) plz showfull work i plead my brain is fried

**Calculus**

which of the following is equivalent to integral (a,b) k*f(x)+C)dx where k and C are constants k integral (a,b)(f(x)+C)dx ***** intergral (a,b)kdx + intergral (a,b)f(x)dx+ intergral (a,b) Cdx k integral (a,b)f(x)+ integral (a,b) Cdx integral (a,b) kdx * integral (a,b) f(x) dx...

**Calculus**

Find F'(x) for F(x)= integral[from 1 to x] of cos(t^3)dt

**Calculus**

lim (x--> infinidy) x^2/ln(x)= -1 0 1 e does not exist

**Calculus**

Which of the following grows faster than e^x as x--> infinity x^4 ln(x) e^-x 3^x .5e^x

**calculus**

Find the point on the line 4x+2y+5=0 which is closest to the point (-2,-1)

**Calculus**

Find the area bounded by the parabola 8+2y-y^2 and the lines y=-1 y=3

**Pre-Calculus**

Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work. 4x - y + 3z = 12 x + 4y + 6z = -32 5x + 3y + 9z = 20 Please help me..

**Pre-Calculus**

Solve the system by the substitution method. Show your work. 2y - x = 5 x2 + y2 - 25 = 0 I solved the problem but I got it wrong for some reason..can you solve it step by step?

**Pre-Calculus**

Locate the foci of the ellipse. Show your work. x^2/36+y^2/11=1 c^2=a^2-b^2 c^2=36-11 c^2=25 c= ± sqrt25 c= ±sqrt5*5 is this correct?

**Pre-Calculus**

Assume that x, y, and z are positive numbers. Use the properties of logarithms to write the expression 2lnx - 6lny + 1/3ln e^12 as a simplified logarithm. Is this 2lnx - 6lny + 4, or can it be simplified further?

**Pre-Calculus**

How do I find the domain of K(x) = x(32 - 2x)^2?

**Calculus**

A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid

**Pre-Calculus**

Find a polynomial with the zeros -1, 7, sqrt2, and -(sqrt2). Can this be f(x) = x^4 - 6x^3 - 9x^2 + 12x + 14?

**Pre-Calculus**

Find the vertical asymptotes, if any, of the graph of the rational function. Show your work. f(x) = (x-4)/(x(x-4)) (x-4)/x(x-4) the common factors cancel out and all is left is f(x)= 1/x... how do I solve this problem?

**Math (Calculus)**

Find the positive value of the parameter t corresponding to a point on the curve parametrized by {x= t^2 +3 ; y=t^2+t for which the tangent line passes through the origin. I tried with 2t+3 and 2t+1 but it isn't successful

**Math Calculus I**

let f(x)= 6sin(x)/(2sin(x)+6cos(x)) The equation of the tangent line to y= f(x) at a= pi/6 can be written in tthe form y=mx+b where m=? b=? I found the f': (9*(cos^2(x)+sin^2(x)))/(3cos(x)+sin(x))^2 but i don't know how to fill it into the form. Can anyone help me? ...

**Integral calculus**

find the area of the surface generated by revolving about x-axis the upper half of the ellipse 4x^2 + 16y^2 = 64

**Pre calculus**

olve the system of equations using matrices. Use Gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2 I need it explained to me, how do I do this?

**Calculus**

Two ships leave the same port at noon. Ship A sails north at 12 mph, and ship B sails east at 19 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place.)

**Calculus**

Solve the differential equation: dy/dx = (3x^2) / (y+1) with initial conditions x = -1, y = 2 I have: ∫y + 1 dy = ∫3x^2 dx (y^2 / 2) + y = x^3 + C (2^2 / 2) + (2) = (-1^3) + C? 4 = -1 + C 5 = c (y^2 / 2) + y = x^3 + 5 Is this correct?

**Calculus**

Volume created when the area bounded by the curve y = 1/x, the x-axis, and the lines x = 1 and x = 4 is rotated about: a) the x-axis: 2.356 units^3 Is this correct? b) the line y = 5 I'm not sure how to do this one.

**Calculus**

when x intercept -3, point P(2,5,7) and Q(1,10,14) how to find x,y and z?

**MATH - CALC**

Use calculus and algebraic methods to do a complete analysis (i.e., intervals of increase and decrease, intercepts, critical points, points of inflection, and intervals of concavity) for each of the following functions and then sketch a graph of the function. (19 marks) ƒ(x...

**Calculus**

Solve the differential equation dy/dx = √[(x^3)(y)] with initial conditions x = 1, y = 2 so far i got y = (x^5)/25 + c so do i plug in 2 = (1^5)/25 + c 2 - (1/25) = c c = 49/25 = 1.96 is this correct?

**Calculus**

A particle with an initial velocity of -6 has its acceleration defined by a(t) = 2t+1. t is in seconds. find: a) its velocity equation b) the total distance traveled by the particle during its first 5 seconds of travel a) v(t) = t^2 + t - 6 b) 24.17 units is this correct?

**calculus-again frustrated-looking for steve asap**

if sinh(y)=[4sinh(x)-3)/(4+3sinh(x)] show that dy/dx=5/(4+3sinh(x)] step plz i plead

**calculus-help me sir~steve**

show that 2f''(t)-f'(t)-f(t)=sin(t)-cos(t) where f(0)=f'(0) has the solution (-2/5)e^(-t/2)-(1/5)sin(t)+(2/5)cos(t) using laplace tranformation plz plz plz show step by step

**Calculus**

Find the area of the region bounded by the curves y = x^(-1/2), y = x^(–2), y = 1, and y = 3. a) (1/2)(3)^1/2 + (4/3) b) 2*(3)^1/2 - (8/3) c) (1/2)(3)^1/2 - (32/3) d) 2*(3)^1/2 - (32/3) e) (8/3) - 2*(3)^1/2 So one thing that is throwing me off on this question is that I ...

**Calculus**

Design an Advanced U substitution problem whose answer must be exactly 6 and can be solved without using calculator?

**calculus-help.. .Me**

if y=e^(-kt)[Acosh(qt)+Bsinh(qt)] where A,B,q and k are constant show that d^2y/dt^2+2kdy/dt+(k^2-q^2)y=0 step plz thanks

**integral calculus**

A cylindrical tank of radius 3 ft length 8 ft is laid out horizontally .The tank is half full of oil that weighs 60 pounds per cubic foot. a.)determine the work done in pumping out oil to the top of the tank. b.)determine the work required to pump out the oil to leave 4 feet ...

**Calculus**

please solve it let f be the function defined over { 0 , ∞ ) as ∫ f(x) = x(ln(x)-1)^2 for x>0 and let (c) be its representative curve , we admit that f is continous at x=0 a ) determine lim f(x) / x as x approaching 0 b) find lim f(x) as x approaching infinity ...

**calculus**

Find the domain for the particular solution to the differential equation dy dx equals the quotient of 3 times y and x, with initial condition y(1) = 1.

**Calculus (Integration proving)**

Show that 0 <= [(integral)(integral, r to none)sin(pi)xcos(pi)y dA] <= 1/32 where R = [0,1/4]x[1/4]x[1,2]. Thank you.

**calculus**

If the graph of f " (x) is continuous and has a relative maximum at x = c, which of the following must be true? The graph of f has an x-intercept at x = c. The graph of f has an inflection point at x = c. The graph of f has a relative minimum at x = c None of the above is ...

**calculus**

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

**Pre-Calculus**

A drug is administered every 6 hours. The kidneys eliminate 55% of the drug over that period. The initial dose is 210 mg. Repeated dosage is 70 mg What is the “Difference equation”? Find the first seven terms of the of the solution sequence. Round to two digits each ...

**Pre-Calculus**

A drug is administered every 6 hours. The kidneys eliminate 55% of the drug over that period. The initial dose is 210 mg. Repeated dosage is 70 mg What is the “Difference equation”? Find the first seven terms of the of the solution sequence. Round to two digits each ...

**Calculus**

An observer 150 feet from point C, where a weather balloon has been released. The balloon rises vertically at a rate of 8ft/sec/. At the very instant the balloon is 250 above ground how far is it from the observer? How Quickly is it moving away from the observer at that moment...

**Calculus**

A car accelerates from rest at 1.1+2(t^1/2) m/h per second for 9 seconds find velocity after 9 seconds.

**calculus**

use logarithmic differentiation to find dy/dx for: [(x^2)(e^2)(x)] / [3√(2x-5)]

**Calculus**

Write a differential equation equivalent to "A chemical decomposition proceeds at a rate equal to the square of the amount of chemical present"

**Calculus**

find the particular solution of the differential equation that satisfies the conditions: f''(x)=sin(x)+e^(2x) f(0)=1/4, f'(0)=1/2

**Calculus**

solve the equation y'=(sqrt(x))/2y

**Calculus**

given d/dx[f(2x)]=f'(x) and f'(1)=1 find f'(2) the choices are 1/4, 1/2, 3/4, 3/2, or 5/2 if it helpes

**Calculus**

Find the particular solution of differential equations that satisfies the initial condition dx/dy=e^(x+y) x(1)=0 I know you have to get all the y and dy on one side and x and dx on the other so you can intagrate and stuff, but im having trouble getting there

**Differential Calculus**

From a faucet, a constant inflow of water is to fill a conical vessel 15 feet deep and 7.5 feet in diameter at the top. water is rising at the rate of 2 feet per minute when the water is 4 feet deep. what is the rate of inflow in ft^3/min?

**Calculus**

Inflection point of 3y=x^3+3x^2-9x+3

**Calculus**

I need help I have to submit work at 12 est time

**Calculus**

Need help with a few questions

**integral calculus**

Find the area between the curves y=5x and 2y=5x^2

**Calculus question ?**

Are there any horizontal asymptote on a ln natural log function

**Grade 12 Calculus and Vectors**

A homeowner wants to enclose a rectangular garden with fencing The garden will be adjacent to his neighbours lot. There will be fencing on all four sides. His neighbour will be paying for half of the shared fence. What should the dimensions of the garden be if the area is 432 ...

**Pre-Calculus**

Determine the magnitude of the positive vectors from the origin to to the following points. A. (3,4) B. (12,5) C. (3,-2) D. (-7,-3)

**Pre-Calculus**

A population of 20 rabbits is introduced to a small island. The population increase at a rate of 60% per year. (A) Find a function of F(t) that represents the number of rabbits on the island after t years. (B) Suppose 100 rabbits were introduced to the island and G(t) is the ...

**Calculus**

The sum of two positive numbers is 10. Find the numbers if their product is to be a maximum