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Calculus Questions
Consider the following initial value problem. y′ + 5y = { 0 t ≤ 2 10...
Consumers' Surplus The demand function for a certain make of replacement cartridges for a water purifier...
Use derivatives of transforms to evaluate the given Laplace transform. (Write your answer as a function...
The owner of a mid-size company advertises on the radio and in a newspaper. He has...
Let LaTeX: C(x)C ( x ) be the cost in dollar of manufacturing x items. If...
What are the equations of the tangent and normal lines to the following curve: y2+y+x =...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
Find the Taylor polynomial of degree 4, p4(x), about 0 for the function y = e^[x^(2)]....
1. The Taylor series for f(x)=x^3 at 1 is ∞∑n=0 cn(x−1)^n. Find the first few coefficients....
The rate of change in number of items sold is given by ?(?) = −31x^2 +...
a- what is the difference between the derivative of X^n and y^n (explain the followings: how...
Compute the work required to drain, from the top, a cylindrical water tank, with height =...
Given the function f(?) = ?^3 − 9?^2 + 24? − 2, a) Find the critical...
The supply curve for a commodity has the equation p = 0.4 x − 2.5 ,...
Use cylindrical coordinates. Evaluate 6(x3 + xy2) dV, where E is the solid in the first...
.Given: f '(x) = x^2 (x-1) (x-2), a) Find three first order critical values of f(x)....
1. Test the series below for convergence using the Root Test. ∞∑n=1 (4n/10n+1)^n The limit of...
Find the function f(x) such that f′′(x)=12x^2− 2/x^2 and f(1) = 5, f′(1) = 2
a) evaluate the directional derivative of z=F(x,y) = sin(xy) in the direction of u=(1,-1) at the...
Find the dimensions of a rectangle of perimeter 124cm with the largest possible area. (draw the...
A manufacturer estimates that when q thousand units of a particular commodity are produced each month,...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
1. For the following functions, find ∆y (the exact change) and dy (the approximate change from...
The supply equation for a certain tee shirt is x = 3p2 + 2p where p...
Find absolute minimum and maximum of the function F(x)=x^3+x^2-x+2 on closed interval (-3,0)
Use the definition of the Laplace transform to find the transform of: f(t)= at+ b cos(2t),...
The revenue and expense equation for widgets are revenue=100∗quantity−0.3∗quantity^2+0.004∗quantity^3 expense=600+10∗quantity Find the derivative of revenue with...
y^''-4y^'+5y=50xe^-x
A company's revenue from selling x items is given by the function R(x)=44x and it's from...
Let y=300∗1.84^x+250x and z=y^2+y. Find dz/dx when x=6.
Find the volume of the solid obtained by rotating the region bounded by the given curves...
Verify that the function ϕ(t)=c1e^−t+c2e^−2t is a solution of the linear equation y′′+3y′+2y=0 for any choice...
1. Find lim x-0. tan4x/sin5x 2. Find and simplify ?/(?) ?? ?(?) = 1-cos(?)/1+cos(?)
ex---What is the equation of the tangent plane and the normal line to the graph of...
(indefinite integral) integrate e^(-3x)sin(2x)
Consider the equation: x^ 4 + 3xy^3 − y ^4 = 9x^2 y a) find the...
Write down general solution of: 4x^2-2xy+2+(4y-x^2+2)y'=0 x>0, y>0
Given f ' ' ( x ) = 2 x + 6 and f ' (...
A brine solution of salt flows at a constant rate of 10 L/min into a large...
Let 30∗price+3∗price∗quantity+(quantity^2)/100=2000 be an equation relating supply and price for gizmos. Find dprice/dquantity and dquantity/dprice (Use...
Use cylindrical coordinates to find the volume of the solid bounded above by: 3x2 + 3y2+...
Use logarithmic differentiation to find the derivative of the function. y = sin6(x) tan2(x) (x2 +...
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(1,0,0),(0,9,0),(0,0,7).
John is healthy and planning on retiring from the company at the age of 55 years....
5. A group of guinea pigs is to receive 25600 total calories per week from a...
determine the volume of solid object limited by cylinder x2 + y2 = r2 and y2...
Suppose that f(x)=6/x^2−25. (A) List all critical numbers of f. If there are no critical numbers,...
Determine the area where the regions of each graph overlap. r=2sin2θ r=1
Evaluate integral 1/1+x^9 dx as a power series. Give the interval of convergence of the power...
My pension plan is an annuity with a guaranteed return of 5% per year. (Assume compounding...
1) Point R has cylindrical coordinates (5, pi/6, 4). Plot R and describe its location in...
Find the integral that represents the volume of the solid bounded by the planes y =...
Calculate the volume bounded by the plane x + 2y + 3z = 6 by coordinate...
You go to the doctor and he gives you 16 milligrams of radioactive dye. After 12...
please show all work Evaluate each of the following limits, for after lim the part with...
The rate of growth of sales (sales per day) for a particular company is predicted to...
Find the volume of the object under the z = x² + y² paraboloid, above the...
Find the equation of the tangent line to the curve defined by the equations x=tln(t), y=sin2(t)...
1. (1 point) Calculate κ(t)κ(t) when r(t)=〈3t^(−1),5,1t〉 κ(t)= 2. (1 point) Find the arclength of the...
Find the flux of the vector field F(x, y, z) = x, y, z through the...
Cartesian Vectors (Write True or False) 1. Geometric vectors have both magnitude and direction but Cartesian...
1. Find T5(x): Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0. T5(x)= Using...
( PARTA) Find the dimensions (both base and height ) of the rectangle of largest area...
Calculate the left Riemann sum for the given function over the given interval, using the given...
A rectangular pen with 5 parallel internal partitions is to be constructed so that the total...
A rectangular storage container with an open top is to have a volume of 14 cubic...
Consider the function f(x) whose second derivative is f′′(x)=6x+10sin(x). If f(0)=2 and f′(0)=4, what is f(x)?
a rectangular storage container with an open top is to have a volume of 10 cubic...
For the method of undetermined coefficients, the assumed form of the particular solution yp for y''...
Use the Midpoint Rule for the triple integral to estimate the value of the integral. Divide...
A company produces a special new type of TV. The company has fixed costs of $466,000...
1. ∫3xe^4x dx = 2. Use integration by parts to evaluate the integral: ∫2s cos(s)ds
Use the gradient to find the directional derivative of the function at P in the direction...
1. Evaluate the limit lim x→0 sin4x /7x 2. In which limits below can we use...
Find a power series representation for the function. (Give your power series representation centered at x=0x=0.)...
Find the tangent plane to the surface z = cos(xy) when (x, y) = (π, 0).
Use the appropriate chain rule to find ??/?? and ??/?? if ? = ?^2 + ?^2...
f(x)=x3-6x2+9x+2 on interval [2,4] Find any local and absolute extreme values of the function on the...
Find the tangential and normal components of the acceleration vector. Then find the speed of the...
Find the derivative of the function. h(t) = (t + 4)2/3(3t2 − 2)3
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