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Find the equation of the plane that passes through the point (2,1,3) and contains the line...
Find the equation of the plane that passes through the point (2,1,3) and contains the line...
Find the equation of the line that passes through the point (2,3,4) and is perpendicular to...
Find the point of intersection of the line (x-2)/-3 = (y-2)/6 = z-3 and the plane...
What is the projection of the unit vector of the direction of the line x= 1...
Let F⃗=xi⃗+(x+y)j⃗+(x−y+z)k⃗ . Let the line l be x=t−1, y=3−4t , z=1−4t . (a) Find a...
Verify that the Divergence Theorem is true for the vector field F on the region E....
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i...
Evaluate the line integral C F · dr, where C is given by the vector function...
A man is filling a pot with water, and it is not yet full. He turns...
Given that y′ = Ay(1 − y ) has a solution satisfying y(0) = 12 and...
1. Find the area bounded by f(x)=3x^2-4 and y=0 for 0 < X < 1. A....
Let S be the part of the plane 2x+5y+z=3 which lies in the first octant, oriented...
Use the following table to estimate ∫0 25 f(x)dx. Assume that f(x) is a decreasing function....
Suppose that f(x)=x+6/x−1 is differentiable and has an inverse for x>1 and f(2)=8. Find (f−1)′(8).
Find the equation of the tangent line to the given curve at t x= 4 cos...
The marginal cost function of producing q mountain bikes is C′(q)=6000/.3q+5. (a) If the fixed cost...
Find the future value of a $40,000 annual income stream if it is invested immediately as...
The tangent line to the graph of y = h(x) at the point (-7, 6) passes...
2)(20 pts.) Find the general solution of the non-homogeneous differential equation y^(4) −4y^(3) +15y′′ −22y′ +10y...
The vector field ?(?, ?) = (? − 3?)?⃗ + 2??⃗ represents an ocean current. Suppose...
Estimating Overall change in Position An object moving along a straight line has a velocity function...
Show that the vector field F(x,y,z)=(−5ycos(−5x),−5xsin(−5y),0)| is not a gradient vector field by computing its curl....
Answer the following questions about the function whose derivative is f prime (x)equals3x(xplus3 ). a. What...
find the minimum and maximum values of y=x^3-9x+8 on the interval [-3,1]
Suppose that a steel company views the production of its continuous caster as a continuous income...
A corporation manufactures candles at two locations. The cost of producing x1 units at location 1...
Use Stokes’ theorem to find Z Z S (∇ × F) · dS where F =...
dy/dx=5y/x^3 where y(8)=e. Find the particular solution.
Find the derivative of √x^sin x
Laplace Transformation Question f (t) = (t − 3)u2(t) − (t − 2)u3(t) Explain in detail...
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of...
use the method of Lagrange multipliers to find the absolute maximum and minimum values of the...
Solve the following differential equation using the method of Laplace Transforms. ? ′′ + 2?′ +...
Solve the given nonlinear plane autonomous system by changing to polar coordinates. x' = −y −...
(a) Estimate the area under the graph of f(x) = 4 cos(x) from x = 0...
Y(s)= 5s2+8s+5 /s2/(s2 +2s+5) Find y(t)=? using partial fractions and laplace transform
Two types of bullets are produced in an arms factory; tracer-bullet and maneuver bullet. One tracer-bullet...
Find the volume of the solid obtained by rotating the region bounded by y=x^2 and y=2x...
Please explain each step, thanks Use the shell method to find the volume about the y-axis....
Determine the area of the shaded region bounded by yequals=minus−xsquared2plus+88x and yequals=xsquared2minus−44x.
Consider the differential equation: . Let y = f(x) be the particular solution to the differential equation...
In the figure to the right, the equation of the solid parabola is yequals=xsquared2minus−1414 and the...
An employee of ‘Sound Limited’ was asked to create a speaker box with a volume of...
The Mary Ellen Candy Company produces chocolate Easter bunnies at a cost per unit of 0.40...
Suppose that a company's daily sales volume attributed to an advertising campaign is given by the...
A strawberry farmer will receive $37 per bushel of strawberries during the first week of harvesting....
For each function, determine the long run behavior x^3+1/x^2+2 has Select an answer A.No horizontal asymptote...
whats the convergence set of this power series? (no derivatives needed) f(x)= 1/(2-x)
How do you use the ratio test to first find the ratio of convergence and then...
Given the function and the bounded interval, f x( )= x3 −6x2 − 45x+ 4 [-5,10]...
Find the coordinates of the absolute maximum and absolute minimum of fx=2x3-3x2-36x on the interval [-3,...
f(x)=ln(1+2x), a=4,n=3,3.7<=x<=4.3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f Tn(x) when x...
What is the meaning of convergent and divergent series? Explain your answer with example.
Mine tailings which has been heated to 110°C in the oven is cooled at room temperature...
11. Using the limit definition of the derivative, find ? ′ (?) for ?(?) = 4√?.
(a) Find the Maclaurin series expansion for f(x) = e 3x and prove that it converges...
Find the area of the region that lies inside the first curve and outside the second...
A manufacturer of bicycle helmets estimates that the monthly cost to produce q helmets is ?(?)...
The population P of bees in a certain area increases at a rate proportional to the...
A Norman window has the outline of a semicircle on top of a rectangle, as shown...
3)Calculate the average rate of change of the given function over the given interval x 0...
Pack-Em-In Real Estate is building a new housing development. The more houses it builds, the less...
(1) Write down a 3 × 3 matrix, call it A, which is not triangular (upper...
use the second derivative test to find the relative extrema if any of the function f(x)=x+576/x
A bookstore expects to sell 120 120 calculus textbooks during the next year. It costs $1.65...
A collage arena is the 13,000 seats. Suppose that when tickets are $16, the average attendance...
Find the Laplace transform for the following. (a.) -42(e^(t-4))U(t-4) (b.) f(t) = {t, 0≤t<1; 0, 1≤t<2}...
Find the absolute maximum and minimum of f(x) = x^1/3*(5−x)^3 on the interval [0, 5]. Justify...
Evaluate the surface integral F · dS where F = 5xyi + x^2j + 5yzk and...
Find the local maximum and minimum values and saddle point(s) of the function. If you have...
A cell of some bacteria divides into two cells every 40 minutes.The initial population is 4...
The x-coordinate of the centroid of area in the first quadrant bounded by y =1 -...
Solve the initial value problem: y''−2y'+y=e^t/(1+t^2), y(0) = 1, y'(0) = 0.
Evaluate the surface integral F · dS for the given vector field F and the oriented...
Solve the differential equation with initial value y''−2y'+y=e^t/(1+t^2), y(0) = 1, y'(0) = 0.
Find the absolute maximum and absolute minimum z-values of h(x, y) = 3x + 4y on...
Consider the infinite series: (2/5) + (2*6) /(5*8) + (2*6*10) / (5*8*11) + (2*6*10*14) / (5*8*11*14)...
Sketch the region enclosed by the equations y = tan x, y 0, x= pi/4 ....
a 10-volt battery connected across a parallel combination of a 100 (ohm) fixed resistor and a...
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