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Calculus Questions
Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.)...
A Norman window is constructed by adjoining a semicircle to the top of a rectangular window,...
Intuitively, a function is _____________ over an interval if its graph can be drawn without removing...
What is the value of the second derivative of function y=10cos5x for x=3? I got the...
The power series ∑ an is defined as a1 = 1/2 and an+1=((4n-1)/(3n+2)) an . Determine if...
Limit steps for (1+t)1/t
Problem: A box with an open top is to be constructed from a square piece of...
Sketch the region enclosed by the curves and find its area. y=x,y=4x,y=−x+2 AREA =
f '(−3) = f '(−2) = f '(0) = f '(1) = 0, f '(x) < 0...
Consider: f(x)=ex-3x^2 Use the graphs of f' and f''. 1) What does the graph of f’...
Find an interval of length 0.2 that contains a root of the equation sin(x)= (x)^2 -...
2. Volume (a) Compute volume of the solid whose base is a triangular region with vertices...
a) Find the values of x and y in order to maximize the value of Q....
Question 1. A volume is described as follows: 1. the base is the region bounded by...
Question: Find the arc length of y= ( x^2 / 2) cut by circle x^2 +...
using the increment method or four step rule solve for: Given s=sqrt of t-2, find ds/dt
Differential equations: 1. Initially, a large tank with a capacity of 100 gallons contains 50 gallons...
1. Give an equation for the line in the xy-plane passing through (5, 4) with slope...
The length of a rectangle is increasing at a rate of 5 cm/s and its width...
Write a word story for this problem If total revenue received from the sale of x...
8?^2 = ?^2 (1 − ?^2) gives on x plane ?please take this function's derivative and...
Find an equation of the tangent line to y=cosx at the point (3pi/4, -sqrt(2)/2). Include hand...
Assume that a rocket is following the path y=−4(x−4)2+10y=-4(x-4)2+10, from left to right. (Also assume there...
Evaluate the integral. π/2 sin5(θ) cos5(θ) dθ 0
What particular solution would use to solve the following NHDE using Undetermined Coefficients? DO NOT SOLVE...
A piece of wire 26 m long is cut into two pieces. One piece is bent...
Given that the acceleration vector is a ( t ) = (−9 cos( 3t ) )...
Find an equation of the plane perpendicular to x+y−2z = 1 and that contains the intersection...
Find fhe equation of the tangent lines with slope of 5 a) f(x)= x^3 + 3x^2...
Can someone please show me the steps in how to do this problem please. find dy/dx...
A hemispherical dome of radius 50 feet is to be given 3 coats of paint, each...
Question3: ( You just need to provide the final answer) a）Calculate the area of the region...
R( x )=46 x ,C( x )=50+30 x+0.1 x^ 2 (a) Find P(100) (b) Find the...
1. a) Find a value of x other than 0 such that the vectors <-3x, 2x>...
let r(t)=<cos(2t),sin(2t),3> describe the shape of the path of motion of the object. how far has...
Find the extreme values of f subject to both constraints. f(x, y, z) = x^2 +...
Use a graph and/or level curves to find the local maximum and minimum values and saddle...
find the general solution: y''-2y'-3y=4e2t
Prove that a continuous real-valued function on a compact metric space assumes its maximum value. I...
y=6-2x-x^2 and y=x+6, about the x-axis. Draw the figure, set up the integral needed to find...
A baseball, hit 2 feet above the ground, leaves the bat at an angle of 41°...
find the general solution of the given differential equation: 4y′′−4y′+y=16e^t/2
1) If z=Ln(x2+y2 ) , x=e-1 ,y=et the total derivative dz/dt will become-------------- Select one: A....
find a vector that goes in the same direction of the straight intersection of the planes...
show that the equation x^3 + e^x =0 has exactly one root
Find the local and absolute extreme values of the function f(x)= 5 + 54x - 2x3...
5. Perform the following operations on the vectors u=(-4, 0, 2), v=(-1, -5, -4), and w=(0,...
Find the curvature of r(t) at the point (3, 1, 1). r(t) = <3t, t^2 ,...
2. (12 pts.)If r"(t) = 〈1, t, sin(t)〉 , r'(0) = 〈2, 3, 1〉 and r(0)...
When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes...
f(x,y,z) = xey+z. (a) Find the gradient of f, ∇f. (b) Find the directional derivative of...
Consider two events A and B from the same sample space S. Which of the following...
Examine the function ?(?, ?) = ?3 − 3?2? − 3?2 − 3?2 + 1 and...
A rod with density δ(x)=4+sin(x) (in mass per unit length) lies on the x-axis between x=0...
Consider the function f(x)=xarctan(1/x) if x≠ 0 ,0 if x = 0. (1) Using the defnition...
The dimeter of the base and the height of a cylindrical can are measured, and the...
Evaluate the line integral of " (y^2)dx + (x^2)dy " over the closed curve C which...
] Consider the function f : R 2 → R defined by f(x, y) = x...
a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the...
1. (1 point) Find the distance the point P(1, -6, 7), is to the plane through...
Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE....
Find the intersection of two planes 3x + 2y − 5z = 3 and x −...
The marginal cost of producing the xth box of CDs is given by 10 − x/(x2...
Compute equations of tangent plane and normal line to the surface z = x cos (x+y)...
Find the point on the line 6x+7y+6=0 which is closest to the point (2,0)
a) Given the region bounded by y=1/x, x=7, y=7 and rotating around x=7, find the volume....
Find the equation of the tangent line to ? = 4? 3 − 2? + 5...
Homework #2 Find the point (a, b, c) where the line x = 1-t, y =...
Consider the following function. f(x) = 1/x^2-9 x −3.5 −3.1 −3.01 −3.001 −3 −2.999 −2.99 −2.9...
A company produces a special new type of TV. The company has fixed costs of $492,000,...
Destiny hand-makes trinkets that she sells over the internet. When she sets the price of a...
If a die is rolled 35 times, there are 635 different sequences possible. The following question...
Estimate the minimum number of subintervals to approximate the value of Integral from negative 2 to...
A chemist has three different acid solutions. The first acid solution contains `15%` acid, the second...
Solve the following second order differential equations: (a) Find the general solution of y'' − 2y'...
Solve using the method of Undetermined Coefficients (Annihilator or Superposition: Your choice). ?′′ − 5?′ +...
a ball p = 2 is cut by the z plane = 1. If D is...
(a) The function f ( x ) = x 3 − 4 x 2 − x...
1.Show that near the origin,sinx+siny≈x+y 2.Find the first order partial derivatives of f (x, y, z)...
What is the gradient of the function f(x,y,z) = 5x^2 + 4y^3 + 4z^4 + xyz...
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