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Calculus Questions
Approximate the sum of the series correct to four decimal places, ((-1)^n-1*n^2)/12^n
We denote by X the profit (in USD bn) of Amazon in the first quarter of...
Suppose that the wholesale price of a certain brand of medium-sized eggs, ? (in dollars per...
P 6. (6 pts) Mark each statement as True or False. A. “Suppose that yp is...
A plane flying with a constant speed of 9 km/min passes over a ground radar station...
transform the given initial value problem into an algebraic equation for Y = L{y} in the...
What are the similarities and differences between a sequence and a function?
A cylindrical drinking cup of circular cross section is to contain 12Π sq. in. of material...
The three sides of a triangle are variable in lengths but the perimeter is constantly 75...
What is “the point-at-infinity” in an elliptic curve? Is this point actually on the curve? If...
In the investigation of a murder, a lifeless body was found by Gil Grissom exactly at...
A trough is 8 ft long and its ends have the shape of isosceles triangles that...
8). a) Find an equation of the tangent plane to the surface z = x at...
A sporting goods store sells 100 pool tables per year. It costs $50 to store one...
You are standing above the point (4,5) on the surface ?=20−(?2+3?2). (a) In which direction should...
The demand curve for original Iguanawoman comics is given by q = (418 − p)2 50...
We shall now look at the velocity field: v = v_xi + v_yj = xyi +...
Find dy/dx of y=x^2cos^4(x)
Which of the following has the most critical values? xe^(2x) 4x^3-9x^2-12x+3 4^(4/5) * (x-2)^2 |x^2-1|
Let f(x) = 3sqrtx. Find the linear linearization of f(x) at x=216 L(x)= Use the above...
Find an equation of the tangent to the curve at the point corresponding to the given...
A UFC Octagon has 8 sides, each 12.46’ in length. It is a regular octagon, 30...
The curve C is defined by the vector function: r(t) = 3ti + cos2tj + sin2tk....
For the function f(x)=−3x^3+36x+6 (a) Find all intervals where the function is increasing. Answer: ff is...
The consumer demand equation for tissues is given by q = (96 − p)2, where p...
Differentiate the following functions: A. F(t)= ln((3t+1)^3) / (4t-1)^5) B. y= ln (|6 - x - 3x2|)
Suppose that f(x) = x^2, g(x) = sin(x) and h(x) = e^x. Using the appropriate rules,...
find the equation of the tangent line to the curve y=e^-3x • cosx at the point...
The Brilliant Butler Company wishes to design a serving tray that will contain the most fluids...
The profit P (in thousands of dollars) for a company spending an amount s (in thousands...
Find the absolute extreme if they exist, as well as all values of x where they...
Suppose you operated a tour bus and you book groups of 20 to 70 people for...
Compute the surface area of revolution about the x-axis over the interval [0,π] for y=4sin(x) (Use...
Use python code to solve IVP. Code must print both general and particular solutions. Please paste...
How do I graph a function with the following properties? increasing: (-∞, 1) decreasing: (1, 3),...
y'-y=cosx
Find an equation of the tangent plane to the surface z=1x^2+1y^2+1x+3y−3 at the point (4, 1,...
Sketch the vector field F⃗ (x,y)=−5i and calculate the line integral of F⃗ along the line...
The future value that accrues when $700 is invested at 5%, compounded continuously, is S(t) =...
Evaluate the iterated integral: ∫5,0 ∫6,3 sqrt(x+4y) dxdy
Let w=−2xy+3yz+4xz,x=st,y=est,z=t2 Compute ∂w/∂s(3,−2)= ∂w/∂t(3,−2)=
Find equations of the tangent plane and normal line to the surface z+2=xeycosz at the point...
1. Find the area of the region enclosed between y=4sin(x) and y=4cos(x) from x=0 to x=0.5π...
Find the exact length of the curve. y2 = 4(x + 3)3, 0 ≤ x ≤ 1, y...
prove the statement using the epsilon delta definition of a limit lim x-->2 (x^2-2x+7)=1
Consider the function f(x)=x⋅sin(x). a) Find the area bound by y=f(x) and the x-axis over the...
For tax reasons, I need to create a rectangular vegetable patch with an area of exactly...
3. (5pts) At noon, ship A is 120km west of ship B. Ship A is sailing...
Find the equations of the tangents to the curve x = 6t2 + 6, y =...
Find the radius of convergence, R of the series. And find the interval of, I, of...
Let f(x)=〖2x〗^3-6x^2-18x+2 Find the interval(s) on which f is increasing and the interval (s) on which...
Solve the equations. Give your answer correct to 3 decimal places 65,000 = 10,000(1.01)8x 72 =...
Prove that √ 3 is irrational.
In 1980 the population of alligators in a particular region was estimated to be 1800. In...
Use Lagrange multipliers to find both the maximum and minimum of the function f(x, y) =...
Consider the vector field ?(?,?,?)=(3?+3?)?+(4?+3?)?+(4?+3?)?. a) Find a function ? such that ?=∇? and ?(0,0,0)=0. ?(?,?,?)= ...
Consider the following initial value problem, in which an input of large amplitude and short duration...
Solve the following equation for x. a)17550=17000 e5 x b)7=2.83 e3 x c)15 ex−3=0.0805 d)4x=19 e)24=10x...
Find y as a function of t if 4y′′+36y′+101y=0, y(0)=9,y′(0)=3. y=
Find the minimum value of the average cost for the given cost function on the given...
Find the absolute extrema of the function on the closed interval. h(s) = 10 / (s...
What is the difference between the maximum and minimum of the quantity a^2*b^2/5, where a and...
Find the inverse Laplace transform of the given function. (Express your answer in terms of t.)...
Find the area of the region within the cardioid r = 1 − cos θ for...
Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min, and its...
A sphere has a radius of 5.44 in., with a possible error of plus or minus...
Write the equation of the tangent line to the graph of y = (x^2 − 16x)/(4x...
Show that the curve y = 4ex + 3x + 2x3 has no tangent line with...
Find the area enclosed by y=ln(x−8) and y=(ln(x−8))^(2). (Use symbolic notation and fractions where needed.) A=
Given r(t)=sin(t)i+cos(t)j−ln(cos(t))k, find the unit normal vector N(t) evaluated at t=0,N(0).
Suppose that at the bucket in the previous problem has a hole in the bottom that...
What is the equation of the curve that passes through the point (0,6)and at every point...
A 20 m rope with mass density of 0.5 kg/m hangs over the edge of a...
Find the volume of the solid generated by revolving the region bounded by the graphs of...
Calculate the ionic strength of the following solution which was prepared by mixing 50 ml of...
Find the volume of a parallelepiped if four of its eight vertices area ? = (0,0,0),...
Find the area of the triangle PQR when P = (-1, 3, 1), Q = (0,...
A company produces a special new type of TV. The company has fixed costs of $488,000...
Show that the equation 2x2 + 2y2 + 2z2 + 10x - 18y = 2 represents...
3 parts use these answers/rules Find the relative extrema of the function Specifically: The relative maxima...
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