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Calculus Questions
Use the Chain Rule to find the indicated partial derivatives. R = ln(u2 + v2 +...
Find the area of the entire region that lies within both curves. r = 3+3sinθ r...
Find the speed of the particle with position function r(t) = (t2 − 2t)⃗i − 2t⃗j...
What is the minimum distance between the curve y=4.5x^3 and the point (2,2) Round your answer...
Find the area of the region inside the circle r = sqrt(3) sinx and outside cardioid...
Solve the special type second order differential equation: x2*d2y/dx^2+x(dy/dx)=1
f(x)= -4x/ x^2+4 i think i found the first dervivative: f'(x)= (4x^2-16)/(x^2+4)^2 but im not sure...
Determine the radius of convergence R, and the interval of convergence l for the series Σn!/(3n)!
find moment of inertia about x-axis of lamina with shape of the region bounded by y=x^2...
The population of a country is growing exponentially. The population in millions was 90 in 1970...
1) Find the angle θ between the vectors a=9i−j−4k and b=2i+j−4k. 2) Find two vectors v1 and...
(a) Find the volume of the parallelepiped determined by the vectors a =< 2, −1, 3...
which of the following is the equation of the plane that is tangent to the surface...
Find the maximum value of the directional derivative of the function f(x,y)=cos(3x+2y) at the point (π/6,−π/8)....
Find the area of the region that lies inside the first curve and outside the second...
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider...
A spring has a natural length of 14 cm. If a 30-N force is required to...
find the area between the curves, y=1-x^2 and y= x^3 + 2x^2 +1
Given vector field ?⃗ =< −?, ?? > on the curve C given ?⃗(?) =< 3...
Consider f(x) = x2 – 8x. Find its derivative using the limit definition of the derivative....
The motion of a spring that is subject to a frictional force or a damping force...
An archer shoots an arrow toward a wall 50 yards away, with an initial velocity that...
A farmer finds that if she plants 55 trees per acre, each tree will yield 20...
If 8200 dollars is invested at an interest rate of 7 percent per year, find the...
1. If you deposit $6,500 into an account paying 8% annual interest compounded monthly, how much...
Find the taylor series for f(x) = ln (1-x) centered at x = 0, along with...
Using Stoke's Thm, find the work done by the vector field F(x, y, z) = 〈z,...
A rectangle initially has width 66 meters and length 55 meters and is expanding so that...
Analyze the graph of ?(?) = 2?3 + 3?2 − 12? + 1. a. Use technology...
A rectangular field with one side along a river is to be fenced. Suppose that no...
Write out the first five terms of the sequence with {[(n+8)/n+1)]^n}^inf n=1 and find its limit...
Find the area of the triangle with vertices: Q(-1,-3,5), R(-2,0,7), S(-4,0,7).
Solve the initial value problem using Laplace transform theory. y”-2y’+10y=24t, y(0)=0, y'(0)= -1
Write a Maclaurin series for the following function; put the answer in sigma notation, and find...
Biologists stocked a lake with 240 fish and estimated the carrying capacity (the maximal population for...
Consider the function f(x)=x4 e-3xShow all work for the following problems. (5a) (3pts) Find all critical...
Solve the given initial value problem D^2x/dt^2 + 9x = 7sin(3t), x(0)=5 x’(0)=0
calculate the surface area of the solid x=sqrt9-y^2 from y=-2 to y=2 which is revolved around...
Set up the integrals for finding the volume of the solid generated by revolving the region...
1. An investment is projected to generate income at the rate of R(t)=20,000 dollars per year...
Use the trapezoidal rule with 4 rectangles to estimate the integral of ex^2 dx from 1...
Angle θ is an angle in the fourth quadrant and cos(θ)=1/3. Find tan(θ)?
A spherical balloon is inflated so that its volume is increasing at the rate of 3.4...
For the function ƒ(x) = -x^2 + 4x + 1 , (a) Calculate the average rate...
A ball is thrown vertically upward from a height of 5 ft with an initial velocity...
Find the maximum profit and the number of units that must be produced and sold in...
5. Le tv=〈1,1,1〉 and w=2i+j−3k. (a) Calculate the following. (i) 4v + 3w (ii) ∥w∥ (iii)...
Find the centroid of the triangle with vertices (0,0), (3,0) and (3,4).
Let S be a surface in the 3-D space (but we don’t have an equation for...
Use integrals to represent the area of the region enclosed by the triangle with vertices (0,−1),...
Consider the function F(x,y)=e^((-x^2/4)-(y^2/4)) and the point P(−1,1). a. Find the unit vectors that give the...
Find Duf at P f(x,y)= sin(3x-4y); P(4, 3); u=(3/5 i-4/5 j) Enter the exact answer. Duf=?
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b onto a....
Illustrate an example keywords absolute extremum and derivative
1-Find two positive numbers satisfying the given requirements. The product is 238 and the sum is...
Find the average value of the function f(t) = 3t^2 - 2t over the interval [-1,3]....
A rectangular swimming pool is to be built with an area of 800 square feet. The...
Write the second order differential equation as a system of two linear differential equations then solve...
Question A: Part of being able to do integrations is choosing a good method without knowing...
The demand for a certain product is Q(x,y) = 200 − 5x2 + 13xy units per...
A rectangular box with an open top is to be made from a 13 -in.-by- 48...
suppose that f'(x)=3x^2+2x+7 and f(1)=11. find the function f(x)
Chemical Mixtures Two chemicals react to form another chemical. Suppose the amount of the chemical formed...
Determine whether the improper integral from 5 to infinity 3/square root x dx converges or diverges,...
Find the maximum and minimum values of the following function, subject to the given constraint. Maximize...
Since the year 2005defense spending (in millions of dollars) in the country of Warpeas can be...
Find the point on the line −3x+4y−1=0 which is closest to the point (2,−1).
The growth rate of a colony of ants is given by the formula 10t(1+t2)2 where t...
1. Determine the producer's surplus for the given supply function and demand level x. (Round your...
A person's average weight increases with height through approximately the end of the teenage years. ...
solve the following ED by reducing it of order: y´´ = 16 + (y)´^ 2
Estimate the area under the curve f(x) = sin(x) from using 6 subintervals and a right...
Consider the line L with parametric equations x = 5t − 2, y = −t +...
Use the shell method to find the volume of the solid generated by revolving the plane...
A manufacturing company of a certain product has a fixed cost of $40 and a variable...
Use differentiation to find a power series representation for the following function: f(x) = x/ (1...
Compute the average value of the function f ( s ) = sin^5 s cos^6 son...
To the best of your ability, measure and record each side of a window in your...
1. Find y' if sin y + 2x^4 = e^x + 4y + xy^3 2. The...
The acceleration of a falling body near the earth’s surface is 9.8 meters per second per...
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