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Calculus Questions
When you're taking an integration by cartesian, does it matter what order you solve in?
Find an equation of the sphere with center (−4, 4, 5) and radius 6. What is...
1.) Given: (3, pi/6) a. Plot the given point b. Rename the given point , one...
Find the surface area of the portion S of the cone ?2=?2+?2, where z≥0, contained within...
A pencil cup with a capacity of 16 in.3 is to be constructed in the shape...
An application of modeling with differential equations from physics
find the Maclaurin series for f(x) and its radius of convergence: f(x) = sin 2x
Find a power series representation for the function; determine the interval of convergence. f(X) = (3x^2)/(5x+1)
Gloria would like to construct a box with volume of exactly 60ft^3 using only metal and...
Let f(x)=x^4(x−5)^8 / (x^2+5)^4 Use logarithmic differentiation to determine the derivative. f '(x) =
find limit x-> infinity (5^x-7^x)/(5^x+7^x) by using substitution
Find the zeros of y = 2sinx+cos2x [0,2pi] Show steps
series of k/k^3-3k+2cosk
Q3. Determine whether the equation (y2cosx - 3x2y - 2x)dx + (2ysinx - x3 + lny)dy...
Find an equation for the plane that contains the line v=(4,−4,−2)+t(3,−3,1) and is perpendicular to the plane...
Find the absolute extrema if they exist, as well as all values of x where they...
For the limit lim x → ∞ x ^5 /e^x How may times will you use...
1) Find the volume of the region under the graph of f (x,y)= 4x+y+1 and above the...
Find the area of the indicated region. We suggest you graph the curves to check whether...
Suppose the position of a particle is given s(t)=(1/3)t3 - t2 - 8t + 10. Determine...
A lamina occupies the part of the disk x2+y2≤1x2+y2≤1 in the first quadrant and the density...
Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by...
If the total cost function for a product is C(x) = 8(x + 5)3 dollars, where...
Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its...
Suppose that a colony of mice started with 50 mice at the beginning of the year,...
Find the volume of the body obtained by rotation of region 0 ≤ y ≤ sin...
Determine the limit of the sequence or show that the sequence diverges by using the appropriate...
A police car traveling (on Golden West St) north toward the corner of Edinger Ave. &...
A metal plate is located in an xy-plane such that the temperature T at (x,y) is...
find a homogeneous linear differential equation with constant coefficients whose general solution is given: c1e^(x)sin4x+c2e^(x)cos4x
A container in the shape of a right circular cone can hold up to 2 Liters...
Consider an object with mass m dropped from rest. Assume that air resistance is proportional to...
Recall that a differential equation is an equation that involves a function and one or more...
Consider the Taylor Series for f(x) = 1/ x^2 centered at x = -1 ...
Find the curvature and the radius of curvature at the stated point. r(t)=4 cos t i+5...
You are the manager of an apartment complex with 50 units. When you set rent at...
Find the intervals of concave up and concave down. State the inflection point(s). ?(?) = (?2?...
The demand for a commodity of a company is given by the demand function: [3+2+1] p...
Use the formal definition of the derivative to find the derivative of given function, ?(?) =...
Find a power series representation for the function. (Give your power series representation centered at x...
A balloon is rising vertically above a level, straight road at a constant rate of 1...
Show that the equation represents a sphere, and find its center and radius.4x2+ 4y2+ 24x+ 4z2−20y=−57...
1. Consider the function f(x) = 2x^2 - 7x + 9 a) Find the second-degree Taylor...
Evaluate the scalar surface integral ∬ S1 (x) dS, where S1 is the portion of the...
6.x3ey-y3lnx=7; dx/dt=1,x=1,y=3
Find the maximum of the following function: h(x, y) = ln(x^20 y^20) given the constraints: 2x^2...
Consider the following initial value problem: x′′−3x′−40x=sin(2t),x(0)=4,x′(0)=3 Using X for the Laplace transform of x(t), i.e.,...
Use the tangent line to approximate the value of ∛26
The radius and the height of a circular cone was measured and found to be 10...
Oil is leaking out of a ruptured tanker at a rate of r=17e2tr=17e2t gallons per hour....
A company needs to make a cylindrical can that can hold precisely 0.7 liters of liquid....
Let r = sin 3θ. Find the equation of the tangent line at θ = π⁄6.
Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the tangent plane at...
How many terms of the series (-1)^n/n! do you need to add up for the partial...
For all integers a,b , c prove that if a doesn't divide then a doesn't divide...
The weekly sales of Honolulu Red Oranges is given by q = 1155 − 21p. Calculate...
You have been hired as a marketing consultant to Big Book Publishing, Inc., and you have...
Problem 3. Find the associated half-life or doubling time for the following models: a. Q =...
6.(a) Determine whether the lines ?1and ?2 are parallel, skew, or intersecting. If they intersect, find...
Solve the initial value problem 9(t+1) dy dt −6y=18t, 9(t+1)dydt−6y=18t, for t>−1 t>−1 with y(0)=14. y(0)=14....
(#9) evaluate integral SQRT(16x^2-1)dx using trigonometric substitution
Solve the initial value problem y′′+6y′+9y=0, y(−1)=3, y′(−1)=3.
Use the ratio test to determine whether∑n=12∞n2+55n converges or diverges. (a) Find the ratio of successive...
Find the equation of the line tangent to the graph of the given function at the...
Differentiate ? = (2?^3 − 5? + 1)^20(3? − 5)^10. Write your answer in simplest factored...
1. This question has several parts that must be completed sequentially. If you omit a part...
One side of a triangle is increasing at a rate of 9 cm/s and a second...
Find c > 0 such that the area of the region enclosed by the parabolas y...
x g(x) g'(x) g''(x) g'''(x) g^(4)(x) 2 17 22 20 14 5 3 50 160/3 141/34...
a) The function f(x)=ax^2+8x+b, where a and b are constants, has a local maximum at the...
Time (months) 0 1 2 3 4 5 Rate pollutants are escaping (tons/month) 4 5 9...
The number of Drosophila fruit flies in a controlled experiment assumes the following growth pattern when...
Calculate two iterations of Newton's Method to approximate a zero of the function using the given...
The region is bounded by y = 2 − x^ 2 and y = x Use...
6.3 2. Let f(x) = x2, and compute the Riemann sum of f over the interval...
Using implicit differentiation complete the following: A) Find dy/dx of x^3 + y^3 =4xy B) Find...
The spread of a virus can be modeled by the following function where N is the...
A large corporation with monopolistic control in the marketplace has its average daily costs, in dollars,...
converges or diverges and for what reason? (n!)/9^(n+1)
1. (30+30) Set up the double integral in polar coordinates with the proper limits that represents...
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