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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
Find the curvatures of the given curves. i: r(t) = ⟨t, t2/2, t2⟩ ii: r(t) =...
Set up, but do not evaluate, the integral for the volume of the solid obtained by...
Curve given below, find the vectors T, N, and B at the point given. r(t) =...
Determine whether the given vectors parallel, orthogonal, or neither. If they are neither parallel nor orthogonal,...
f(x)=4x^3+9x^2−12x−3. 1.Find the interval(s) on which f is increasing. Answer (in interval notation): 2. Find the...
Find the parametric and symmetric equations of the line that is parallel to the line x...
Minimizar f(x,y,z)=x2+4y2+16z2 sujeto a la restricción. Minimize f(x,y,z)=x2+4y2+16z2 subject to the constraint 1=xyz 1=xy 1=x
Find f. f ''(x) = 6 + 6x + 36x2, f(0) = 3, f (1) = 13
Verify that the Divergence Theorem is true for the vector field F on the region E....
Solve the differential equation dy/dx + 4(x^3)y = 8(x^3)
Find the equations of (i) the tangent plane and (ii) the normal line to the surface...
A full rectangular swimming pool with an 18 x 12 feet base and a depth of...
a. Find the first three terms in the power sereis for integral from 0 to x,of...
Find the area of the surface generated by revolving the curve x = ?square root 4y...
Find the centroid of the region bounded by the graphs of the functions y=3x^2, y=x^2+7 The...
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with...
1) Find the maximum and minimum values of the function y = 13x3 + 13x2 −...
A corporation is initially worth 88 million dollars and is growing in value, VV, by 3434%...
In the system AX=b, where A is m x n matrix and rank of A is...
Suppose that a function f has the the following limits. What is true about the graph of...
Find the exact area of the surface obtained by rotating the curve x = 1-2y^2, 1...
Suppose that 5 J of work is needed to stretch a spring from its natural length...
Find an equation of the plane.The plane through the point (6, −5, −1) and parallel to...
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 350...
Find absolute maximum -X^3+3X^2-4 at (-2,1)
Find the absolute maximum of h(x)= x^2 −x−2 over [−3,6]. Enter only the y -coordinate of...
Find an equation of the tangent plane to the surface z = x^2 + xy +...
Use implicit differentiation to find ∂z/∂x and ∂z/∂y if yz + xlny = z^2 .
A trough is filled with a liquid of density 810 kg/m3. The ends of the trough...
A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter...
Please show all work step by step The growth of a bacterial colony is modeled by...
Use cylindrical coordinates. Evaluate the integral, where E is enclosed by the paraboloid z = 8...
1. A volume is described as follows: 1. the base is the region bounded by y=2−...
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