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Calculus Questions
Based on data from 1980 to 2000, the median sales price of a new one-family home...
Consider the curve y = e sin x for π /6 ≤ x ≤ π /3...
The curvature of a circle centred at the origin with radius 1/3 is
The monthly payment for a home loan is given by a function f(P,r,N)f(P,r,N) where PP is...
A baseball team plays in a stadium that holds 56000 spectators. With the ticket price at...
For the given cost function C ( x ) = 44100 + 700 x + x...
Let z = cos (- (5y2 + 2x) ). Then a) The rate of change in...
The supply curve for a commodity has the equation p = 0.4x − 2.5 , and the...
Which of the following is true about the sequence sin((npi)/2)? I.the sequence is abounded II.the sequence...
The planes z+5?+2?-3=0 and 3y+2?+2?+7=0 are not parallel, so they must intersect along a line that...
(a) Use Euler's method with each of the following step sizes to estimate the value of...
Sketch the graph and find the area of the region that lies inside r = 2cosθ...
What is the equation of the osculating plane of the curve X(t) = (sin t, cost,...
When hired at a new job selling jewelry, you are given two pay options: Option A:...
You are choosing between two different cell phone plans. The first plan charges a rate of...
The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while...
On a particular day, the temperature in Tahoe is given by T(?, ?) = uv^2( where...
Find the domain of the function. g(x, y) = 8/x-y a.The domain is the half plane...
Rabbit population P(t) satisfying the following equation d P/ d t = kP(600-P), the initial population...
Use the method of Lagrange multipliers to show that the point on a sphere with positive...
Find the area of the overlap between two circles, both of radius 4 with one centered...
Find the derivative of the function using the definition of derivative. G(t) = 1- 3t /...
A particle moves according to a law of motion s = f(t), t ≥ 0, where...
Eliminate the parameter to find a Cartesian equation of the curve (do so without solving for...
- Suppose f is a function such that f′(x) = (x+ 1)(x−2)2(x−3), so that f has...
5. Find the open intervals on which f(x) =x^3−6x^2−36x+ 2 is increasing, as well as the...
Let σ be the portion of the surface z = 1−x^2 −y^2 that lies above the...
Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three...
1.Let R be the shaded region below enclosed by the y−axis, the line y = x−1...
What mathematical ideas are you curious to know more about as a result of studying the...
3) The base of a solid is the first quadrant region between the curve y =...
The number N of bacteria in a refrigerated food is given by N(T) = 10T2 −...
Solve the following initial value problem. y′′′ − 21y′′ + 135y′ − 243y = 0, y(0) = ...
13. Extend the sketch of the graph of f(x) = cosx + 1x in Example 4...
Use a double integral to find the area of the region in the fourth quadrant that...
Find the area enclosed by the ellipse x2144+y2256=1.x2144+y2256=1. Hint 1: Area can be found using the...
A box with a square base and closed top must have a total surface area of...
Find the place where L(t) = <4+ 3t, 3, -(2+5t)> intersects the 4x-4z = -8 plane.
The population of Pacifica was 1,000,000 people in 2010. The growth in population is given by...
at2y’’ + bty’ + cy=0 (t>0,a,b,c are all real numbers) equation obtained from substituting: A) x=log(t)...
Consider the function f(x) = x 2 − x on [−1, 1]. Find the minimum and...
There is a reservoir of 800,000 tons of water. Currently, the reservoir is said to contain...
For tax reasons, I need to create a rectangular vegetable patch with an area of exactly...
A rectangular room was designed to be built for a length of 10 feet and a...
Find the equation(s) of the tangent line(s) to the graph of the curve y = x3...
Suppose the annual revenue of a startup can be modeled by the equation R(t) = (2t)/(t...
Use a triple integral to find the volume of the given solid. The solid enclosed by...
The velocity of a particle moving along a line is a function of time given by v(t)=81/(t2+9t+18)....
Find the volume of the solid generated by revolving the region bounded by the given curve...
For the function f(x)=x^3+5x^2-8x , determine the intervals where the function is increasing and decreasing and...
For the equation given below, evaluate y′ at the point (1,2). (3x−y)^4+4y^3=33. y′ at (1,2) =
Find the indicated maximum or minimum value of f subject to the given constraint. Minimum: f(x,y)=2...
Find the solution of the initial value problem y′′+5y′+6y=0, y(0)=11 and y′(0)=-25
A Ferris wheel is 15 meters in diameter and boarded from a platform that is 5...
if x^2+y^2=1, find an expression for d^2y/dx^2
if x^4+y^4=1, find the expression for d^2y/dx^2
(a) Find parametric equations for the line through (5, 3, 6) that is perpendicular to the...
Two cars are approaching an intersection on roads that are perpendicular to each other. Car A...
how do I show if the series sigma(n=1 to infinity) cos(npi/3)/(n!) is divergent, conditionally convergent, or...
integral 1/secx-1dx
Given S is the surface of the paraboloid z= 4-x^2-y^2 and C is the curve of...
find the volume of the solid obtained by rotating the region bounded by the graphs of...
The marginal cost in dollars is given by dc/dx=4x +3. If the fixed costs are $2000...
Solve: (x^4 – xy^3)dy + (2y^4 – x^3y)dx = 0
A parametric curve r (t) has the property that r ″ ( t ) = (...
Let R be the tetrahedron bounded by the planes x=0, y=0, z=0 and 33x+7y+2z=8. The volume...
Use implicit differentiation to calculate the slope of the tangent to the curve given by sinh(xe ...
If f(x) = 3x2 − x + 5, find the following f(2) = f(−2) = f(a)...
Discuss the purpose, function, and problems with using the MyPlate Planner.
Find, correct to the nearest degree, the three angles of the triangle with the given vertices....
Find Cartesian equation of a plain through the point a and parallel to the given vectors...
3. Given f(x) = arctan x and g(x) = e^x , find the following: a. (f...
Find the ABSOLUTE MAXIMUM value of the function on the closed interval .
Let P(t) represent the number of people who have been infected by a disease t day...
Use linear approximation to estimate (0.97)3 - 3(0.97)2 without using a calculator.
A one-product company finds that its profit, P, in millions of dollars, is given by the...
Solve the following initial value problem. y′′ − 9y′ + 20y = 3x + e5x, y(0) = ...
Let w = (x 2 -z)/ y4 , x = t3+7, y = cos(2t), z =...
The curve y = x4 - 4x3, where is it increasing, where is the inflection point...
6) You may answer the following questions using the appropriate C(n,r)’s and or P(n,r)’s. It is...
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