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Calculus Questions
Use the shell method to find the volume of the solid generated by revolving the region...
Solve the first-order differential equation by any appropriate method. (Enter your solution in the form F(x,...
Define Exact Equations with suitable example? Define Seperable Equaitons with example. What is Integrating Factor, Give...
(x^3)/(sqrt(4-x^2) without using u- substitution
Find the first four nonzero terms in a power series expansion about x=0 for a general...
At what point on the curve x = 3t^2 + 1, y = t^3 − 3...
y=x, y=9x/(1+x^3), Revolve this around the line x = -1 then find volume of the solid
1. Find the equation of the line going through (2, -1) and (3,7) 2. Anvils are...
How can one use a vector valued function tor represent a curve in two dimensions? Explain...
Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 7)j + zk. Find the...
Solve the IVP: (14y^13 + 8x^3 +42xy^5)dy + (12x^3+24x^2y+7y^6)dx = 0, y(2)=1
Approximate the arc length of the curve y=x^-1 over the interval[2,7] using Simpson's rule and 12...
1. (a) Use the graph paper provided to sketch the region bounded by the x-axis and...
Find the directional derivative of f at the given point in the direction indicated by the...
Let R be the region of the plane bounded by y=lnx and the x-axis from x=1...
solve the given initial-value problem y"-100y=15, y(0)=1, y'(0)=0
Use the position function s(t) = −16t2 + v0t + s0 for free-falling objects. A ball...
1) What is a function? Give two examples 2) Solve x2−4=0 factorize 3) Graph following line...
Use the differential equation (1−x)y''−4xy'+5y=cosx(1-x)y′′-4xy′+5y=cosx to answer the following questions: What is the type of the...
1) find the Taylor series expansion of f(x)=ln(x) center at 2 first then find its associated...
Find an equation for the line tangent to the parabola y= 2x^2 -13x +5 which has...
Give an example of a function that increases concave downward on the interval (0, ∞). Justify...
Find the derivative of each function. (a) F1(x) = 3(x4 + 5)5 2 F1'(x) = (b)...
Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=2^2 , z=x^2+y^2 and z=0.
find the Taylors series for f(×) = In(3 +2×) at a=1
Suppose f′(x) = √(x)*sin(x^2) and f(0) = 5. Estimate f(b) for: b = 0 : f(b)...
Solve the problem. On a hot day, a child can sell 31 cups of lemonade if...
Using Leibniz notation (i.e., ??/??, ??/??, etc.), find derivatives for each of the following functions. You...
What is the area between the curves y=−x^2+4 and y=−3?
(10 marks) Solve the second-order linear differential equation y′′ − 2y′ − 3y = −32e−x using...
Find the radius of convergence and the interval of convergence of the power series. (Please check...
Calc 2: Please make sure these are right!! Find the exact length of the curve. x...
Find the number(s) k such that the average value of f(x)=sin3x cos3 x-k on the interval...
Find the solution of the exponential equation (Enter your answers as a comma-separated list.) 3^(2x −...
Find the work it would take to build a limestone pyramid with a square base with...
Find the orthogonal trajectories of the family of curves. ?2 = ky
1. a) an ornamental light bulb is designed by the revolving graph of y=(1/3)x^(1/2) -x^(3/2), 0<x<(1/3)...
(a) Show that the parametric equations x = x1 + (x2 − x1)t, y = y1 +...
[2 marks] Find the derivative of y = √ 4 sin x + 6 at x ...
If z = x2 − xy + 7y2 and (x, y) changes from (3, −1) to...
Let f (x) = −x^4− 4x^3. (i) Find the intervals of increase/decrease of f . (ii)...
Use Lagrange multipliers to find the point on the plane x − 2y + 3z =...
Please let this pass, Just now i wrong uploaded, i want to refund this question ,...
Calculate the line integral of the vector field ?=〈?,?,?2+?2〉F=〈y,x,x2+y2〉 around the boundary curve, the curl of...
Find the direction cosines of v=8i-8j+4k and confirm that they satisfy cos2α+cos2β+cos2γ=1. Then use the direction...
Calculate the volume of the rotational object formed by rotating the given curve with the parametric...
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>...
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