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Calculus Questions
evaluate the integral. (4x-6) sqrt(2x^2-10x)
Solve the differential equation (1-y)dx-x^2y^2dy=0
solve the initial value problem using Laplace transform x"(t)+3x'(t)+2x(t)=t x(0)=0 x'(0)=2 differntial equations
Use Hooke's Law to determine the work done by the variable force in the spring problem....
write a ellipse in standard form by completing the square and then give th ordered pairs...
∫2?/? (2 + ln(?) )^2/? ??
Let a = <2, -9, -2> and b = <-3, -2, -7> vectors. Find the scalar...
Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz...
each side of a cube is increasing at a rate of 4 cm/s at what rate...
Using the Intermediate and Mean Value Theorems, show that the equation x^3 - 15x + c...
Find the exact global maximum and minimum values of the function f ( x ) =...
Compute the area bounded by x² + y² = 4 , x² + y² = 4x...
Use the method of cylindrical shells to find the volume generated by rotating the region bounded...
Approximate the fixed point of the function to two decimal places. [A fixed point of a...
Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two successive...
The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q =...
A one-product company finds that its profit, P, in millions of dollars, is given by the...
Integrate f(x,y,z) = z over the region enclosed by x^2+y^2=3^2 , z=x^2+y^2 and z=0.
Corn is being poured through a chute at the rate of and falls into a conical...
Let F(x, y)= xy. consider the constraint 2x^2 + y^2 =36. what are the maximum and...
find a value of x other than 0 such that the vectors <-3x, 2x> and <4,...
Homework #4 Find a vector that goes in the same direction of the straight line of...
find the differential equation using laplace transform. y'' + 4y = 15et
Draw a contour map of the function f(x, y) = y/(2x 2 + y 2 )...
1) Solve the given differential equation by finding, as in Example 4 of Section 2.4, an...
y^''-y^'-2y= e^t , y(0)=0 and y^'(0)=1 Solve by using laplace transform
1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli...
If f(x, y) = 49 − 7x2 − y2 , find fx(1, 2) and fy(1, 2)...
Find an equation of the tangent plane to the given surface at the specified point. z...
Find the maximum and minimum values of the function f(x,y,z)=3x−y−3 subject to the constraints x^2+2z^2=324 and...
1. Find the radius of convergence for: ∞∑n=1 (−1)^n x^n / √n+9 2. If f(x)=∞∑n=0 n...
find the area of the part of the circle r=4sin(theta) +cos(theta) in the fourth quadrant.
A graphing calculator is recommended. Use Newton's method to find all solutions of the equation correct...
differential equations!! y'' +y' +2xy= 0 ,what is the solution for the differential equation's Power series...
Decide whether the given line and plane intersect or not. If yes, find the point of...
Analyze the function f and sketch the curve of f by hand. Identify the domain, x-intercepts,...
(b) Solve the separable differential equation y'= (7e^-3x+2x^2-xcosx)/-6y^3 &nb
Use laplace transform to solve y''+y' = 5
A tank contains 80 kg of salt and 1000 L of water. Pure water enters a...
Consider the following differential equation: dy/dx = −(3xy+y^2)/x^2+xy (a) Rewrite this equation into the form M(x,...
Consider the differential equation y' = x − y + 1: (a) Verify that y =...
You are given a differential equation x[n+2] + 5x[n+1] + 6x[n] = n with start values...
(a) If $1400 is borrowed at 7% interest, find the amounts due at the end of...
The demand for a product is given by p = d ( q ) = −...
Suppose a company has fixed costs of $700 and variable costs per unit of 7 8...
A small candy store makes three types of party mixes. The first type contains 40%nonpareils and...
Find the maximum and minimum of ?(?, ?) = 16? 2 + ? 2 subject to...
Find an equation of the tangent line to the curve at the given point. 1.) y=...
Find the volume of the parallelepiped determined by the vectors a, b, and c. a =...
Solve the following systems of differential equations:
name and/or explain 1 way an integral might be used in business calculations.
Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) f(x) =...
The wholesale price p of e-tablet writing styluses in dollars is related to the supply x...
For the following functions. Determine the location of all critical point(s) and their nature. f(x)=1⁄3x3 –2x2...
A conical container of radius 6 ft and height 24 ft is filled to a height...
Question 30. Find the global maximum and minimum values of f(x) = x − 3x1/3 over...
find the total differential (a) f(x,y)=x^2+3xy+2y (b) f(x,y)=x-y/x+1
Find the Area Between the Curves x=-3 , x=4, y=2e^2x, y=e^2x +1
When three complex numbers z1 z2 and z3 satisfy the following equation z3 - z1 =...
By about what percentage will the edge length of an ice cube decrease if the cube...
find the equation for the tangent line to the function f(x) = x^4 - 9x^3 +...
(M -at)dv/dt - ab = -g(M - at) Determine the height at time t
Find the exact extreme values of the function z = f(x, y) = x^2 + (y-19)^2...
f(x) = x^2+1 -Estimate area between graph f(x) & x-axis -interval : [1,3] - n=4 rectangles...
Determine whether Rolle's Theorem can be applied to the function f(x) = x^4-2x^2 [-2,2]. if not...
A lamina with constant density ρ(x, y) = ρ occupies the given region. Find the moments...
What is the difference between exact and inexact differentials?
Find the absolute maximum and minimum values of the function over the indicated interval, and indicate...
Use spherical coordinates. Evaluate (2 − x2 − y2) dV, where H is the solid hemisphere...
Find an equation of the tangent plane to the given surface at the specified point. z...
(i) Given the function f(x) = x3 − 3x + 2 (a) What are the critical...
Find a vector equation of the line of intersection for the given pair of planes. Remember,...
Write equivalent Cartesian equation for the conic r = 1 / (3+cos θ) . Identify and...
Determine the equations of the lines that are tangent to the ellipse x2 + 4y2 =...
Consider a wire of length L which is to be cut into two separate pieces. The...
If you currently have $1 in the bank and person A pays you 5% interest compounded...
A lamina occupies the part of the disk x2 + y2 ≤ 9 in the first...
Find the slope of the tangent line at each given polar curve at each point specified...
Use the z-transform method to solve the following difference equation: y[n + 2) = 3y[n +...
Find the Taylor series for f(x) centered at the given value of a. [Assume that f...
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