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Calculus Questions
Assume that the strength of a long object like a tree trunk or a steel beam...
Compute the following limits and show all your work: (a) A = lim x→∞ [3x^2 −4/x^2...
Consider the function f(x)=4x2-x3 provide the graph the region bounded by f(x) and the x-axis over...
solve the ODE solving for the general solutions y''+y'-12y=sin(t)e^(3t)
Suppose that ff is a Riemann integrable function on [0,2][0,2] and that ∫20f(x)dx=5∫02f(x)dx=5. Suppose further that...
suppose you have a cardboard of area 36sqrt(3)m^2 and you need to make a triangular prismatic...
Sketch the region enclosed by x = 56 − y^ 2 and x = − y...
Suppose that f(4) is continuous and f′(c) = f′′(c) = f′′′(c) = 0, but f(4) is...
solve the linear order y' - 2y = cos(3x). solve for y.
solve the separable differential eq. y'=(y-3)(y+2)/(x-2)(x=4). solve for y.
A cylindrical can is built to store a food. This can is constructed without a lid...
1. Find the limit as n goes to infinity of xn over n factoiral.
Identify any extrema of the function by recognizing its given form or its form after completing...
Assume the acceleration of the object is a(t) = −32 feet per second per second. (Neglect...
Suppose you deposit $2000 at 4% interest compounded continously. Find the average value of your account...
A function f, a closed interval [a, b], and a number of equally spaced subintervals n...
Find the Taylor Series of the given function centered at the indicated point. x^4 at a...
A 50-foot ladder is placed against a large building. Unfortunately, the base of the ladder is...
Draw an oriented curve C and a vector field F along C that is not always...
find all values of a such that distance from (1,2,a) to the xy-plane equals distance from...
Find the Taylor Series at a=pi/2 for f(x)=5cos(x).
write and evaluate the triple integral for the function f(x,y,z) = z^2 bounded above by the...
Parametrize the curve r(t) = <5sin(t), 5cos(t), 12t> with respect to arc length, measured from the...
Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.)...
A Pyramid is 655 ft high (due to erosion, its current height is slightly less) and...
A cyclist leaves her house at 8:00AM and begins travelling directly east at 20 km/h. Fif-...
Consider the parametric curve given by x = t + ln t, y = t -...
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6?...
Find f. f ''(x) = −2 + 24x − 12x2, f(0) = 2, f '(0) = 14
An open box is to be made from a 20 cm by 29 cm piece of...
1) A cylindrical tank with a radius of 10 feet and a height of 20 feet...
(calculus)Water is leaking out of an inverted conical tank at a rate of 12000.0 cm3/min at...
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the...
Find a particular solution to each of the following differential equations with the given initial condition:...
g(x)= (x^2 +1)^3 (x^2+2)^6, for this question I need to find the derivative of 32x.
Suppose we have a rectangular tank buried upright so that the top is 7ft underground. The...
Let P be the plane given by the equation 2x + y − 3z = 2....
1)A perfectly spherical snowball melts in such a way that its surface area decreases at the...
Find an equation of the tangent line to the curve at the given point. A) y...
A detector measures a positron moving through an electromagnetic field along a path given by r...
Find the equation of the tangent to the curve y=x(x+1)(x+2) at x=2 on curve
find the point on the graph of the function that are closest to the given point....
Find the slope of the tangent line to the given polar curve at the point specified...
Suppose the velocity of a car (in mph) driving out of Houston at t (in miles)...
let a, b and c be constants. For the first problem, a sine wave is any...
Use Lagrange multipliers to find the extremal values of f(x,y,z)=2x+2y+z subject to the constraint x2+y2+z2=9.
Notice that ln(20) is slightly less than 3? Use a linear approximation to estimate f(3)=e^3 using...
Describe the primary components and features of a Fourier Series.
1.A child is on a swing. At its highest point, the swing is 5 feet above...
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an...
How to set up intergration of this problem --finding the volume of the sphere x^2 +...
Use the given transformation to evaluate the integral. 6y2 dA, R where R is the region...
Let C be the circle with radius 1 and with center (−2,1), and let f(x,y) be...
Verify the quotient rule for each of the following: 1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2 2. f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1
Which of the following (horizontal) planes is tangent to the surface z=x2+2xy−y2+6x+6y+3z=x2+2xy−y2+6x+6y+3? Select one: a. z=-4...
Find the area of the following part of the surface z = x + y2 that...
The function f(x, y) = x^−2 y^3 is a potential for a vector field F. Use...
Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased...
find the general solution of the differential equation: y' + 2y = te^−4t. Use lower case...
Find the mass and center of mass of the lamina that occupies the region D and...
Find the first five nonzero terms of the Maclaurin expansion. f(x) = e^x/(1+x)
Find the directional derivative of the function f (x, y) = tan−1(xy) at the point (1, ...
The average value of a positive function over an interval [a,b] is given by the area...
Given a trough with length y, and an end which is an isosceles right triangle with...
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for...
The local maximum value of the function f(x,y) = x2 + 2y2 − 2xy − 4y...
Determine if the following statements are true or false. If it is true, explain why. If...
If 5x^2+3x+xy=3 and y(3)=-17, find y'(3) by implicit differentiation. Thus an equation of the tangent line...
Find the cost function for the marginal cost function. C′(x)=0.03e^0.05x fixed cost is $9
The volume of a right circular cylinder is given by V= πr2h, where r is the...
solve for x(t) and y(t): x'=-3x+2y; y'=-3x+4y x(0)=0,y(0)=2
Let f(x)=22−x2f(x)=22-x2 The slope of the tangent line to the graph of f(x) at the point...
The number of people taking city buses at price p dollars per ticket is given by...
Determine the maximum curvature for the graph of f(x)=8ln(2x). The maximum curvature is ___ at ___
The temperature at a point (x, y, z) is given by T(x, y, z) = 10e^(− ...
Researchers have shown the density d(x) of the Dead Sea brine (in g/cm3) during evaporation can...
The demand function for a Christmas music CD is given by q=D(p)=0.25(225−p2)where q (measured in units...
Suppose that f is a twice differentiable function and that its second partial derivatives are continuous....
Find the limits, or state that the limit does not exist (you must justify answer): a)...
A function y(t) satisfies the differential equation dy dt = y4 − 11y3 + 24y2. (a)...
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