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Calculus Questions
find the 101st derivative of y=x*e^x
The weekly demand function for x units of a product sold by only one firm is...
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for...
A trough is 8 ft long and it's ends have the shape of isosceles triangles that...
Differentiate the function: s(t) = 9t − 3(2t4 + 5)3 s'(t) = Could you also explain...
(Integration Application) A water tank is shaped like an inverted cone with a height 2 meters...
refer to the graph of y=f(x)=x^2+x shown a. Find the slope of the secant line joining(-3,f(-3))...
Suppose that the total cost function, in dollars, for the production of x units of a...
Find the radius of the curvature of the following curve at the given point. Then write...
Use polar coordinates and double integrals to compute the improper integral: sqrt{x} (e^{-x) dx.
Using rectangles whose height is given by the value of the function at the midpoint of...
Marketing research has found that at a price of $179.95 per unit, sales would be 175,000...
Evaluate the surface integral S F · dS for the given vector field F and the...
Consider two curves: r =1, r = 2sindeta . Find the intersection area A. Show work...
Find the absolute maximum value of f(x)= x4−2x a) 0 b) −1.1906 c) No absolute maximum...
Use logarithmic differentiation to differentiate the following function. f(x)=(x+7)5(5x-2)4 f'(x)=___________
Find a cubic function f(x) = ax3 + bx2 + cx + d that has a...
(1 point) Find the minimum speed of a particle with trajectory c(t)=(t^3−4t,t^2+1)
Mass of a Moving Particle The mass m of a particle moving at a velocity v...
5) Let ℎ(?, ?) = ???^x . Classify all local extrema of the surface using the...
Use Euler's Method with step size 0.12 to approximate y (0.48) for the solution of the...
A chain lying on the ground is 10 m long and its mass is 60 kg....
Solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the form...
Find fxx(x,y), fxy(x,y), fyx(x,y), and fyy(x,y) for the function f f(x,y)= 8xe3xy
Company A is trying to sell its products as the following options. - each product cost...
Find the absolute maximum and minimum values of the function over the indicated interval, and indicate...
Use a double integral in polar coordinates to find the volume of the solid bounded by...
Show that F=(tany, xsec^2y) is conservative and then calculate the work required to move any object...
A tank is initially filled with 1000 litres of a salt solution containing 1000 grams of...
Use finite approximations to estimate the area under the graph of the function f(x) = 24−x2+2x...
The curve given by the parametric equations of x = 1-sint, y = 1-cos t ,...
Find the volume of the area bounded by the surface z = 4 - x2 on...
Consider the function f(x) whose second derivative is f''(x)=2x+5sin(x). If f(0)=3 and f'(0)=2, what is f(5)?
Sketch the region R bounded by the graph of y=1-(x+2)^2 and the x-axis. Set up, but...
Let . Use the definition of derivative and the Procedure/Example table in this section to verify...
Use finite approximations to estimate the area under the graph of the function f(x) =8−x2+2x between...
Write the C55x assembly code for each of the following C snippet code shown below. Assume...
How can I prove that the Maclaurin series of (1+x)^k equals to the binomial expansion with...
Of all the rectangles with an area of 1296 square feet, find the perimeter of the...
H8-13 Helium is pumped into a spherical balloon at a rate of 2 cubic feet per...
Use a triple integral to find the volume of the solid enclosed by the paraboloids y=x2+z2...
Find dy/dx and d2y/dx2 for the given parametric curve. For which values of t is the...
A company is planning to manufacture cylindrical above-ground swimming pools. When filled to the top, a...
a= 1, b =6 , c= 4 T(x,y,z) =(x^2 )y +(y^2 )z Find the directional derivative...
There is a war going on. there are 100 people in the circle, the first person...
Estimate the area under the graph of f left parenthesis x right parenthesis equals 5 x...
Vector j is parallel to vector h (-9.3, -22.1, -13.6) and passes through d (10,10,10). Find...
Find the maximum profit and the number of units that must be produced and sold in...
The relationship between the amount of money x that a company spends on advertising and the...
laplace transform x''(t) - x'(t) - 6 x(t)= e^(4t), x(0)=1, x'(0)=1
Suppose f is a function with f(1) = f′(1) = ··· = f^(9) (1) = 0,...
Let X be the region bounded by y=x and y=x^2. Find the volume of the solid...
A fence is to be built to enclose a rectangular area of 270 square feet. The...
A plane flying horizontally at an altitude of 2 mi and a speed of 540 mi/h...
2-Verify the given linear approximation at a = 0. Then determine the values of x for...
d2ydx2-4dydx+4y= e2x1+x
Find the volume of the generated solid when the region bounded by the graphs of the...
Evaluate the line integral, where C is the given curve. xyeyz dy, C: x = 2t, y =...
Continuity and the derivative: 1A) Show that there exists a real root of the equation in...
Mark each series as convergent or divergent 1. ∑n=1∞ln(n)4n 2. ∑n=1∞ 4+8^n/2+3^n 3. ∑n=1∞ 6n/(n+3) 4. ∑n=1∞1/(7+n2−−√6)...
Let R=[0,1]×[0,1]. Find the volume of the region above R and below the plane which passes...
Set up, but do not evaluate, an integral to find each of the following: a) The...
Let f(x) = x^3 - x a) Find the equation of the secant line through (0,f(0))...
let f(x)= √x ln(x). find the interval on which f is concave upward.
Find the equation of the tangent line to the graph of ?(?) = cos ? at...
If point A is (4, 2, -3) and B is (6, -3, 5) 1. Write an...
Find each of the following functions. f(x) = 4 − 4x, g(x) = cos(x) (a) f...
Describe both the transient and the steady-state solution of the forced spring-mass system: x'' + 2x'...
(1 point) Find the area under one arch of the trochoid x=8θ−4sin(θ),y=8−4cos(θ).
Let the nth term of a sequence be given by an = sin(n2)/n for n ≥...
A) Find the first 4 nonzero terms of the Taylor series for the given function centered...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy...
Evaluate definite integral (0 to pi/2) secxtanx-sec^2(x) dx
Find the flux of F across S, S F · N dS where N is the...
find all values of y such that the distance between (6,y) and (-5,8) is 20
Solve the following system of differential equations. Express your answer as functions of x and y...
Given ?(4, −2,5), ?(3, −3,1) and ?(5,2,8), determine the vector equation, parametric equations and the scalar...
With a 20 meter long fence, it is desired to create a trapezoidal region with a...
Some kids are starting an orange juice stand. Including the supplies to set up and decorate...
Use the first derivative test to determine the location of each local extremum and the value...
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