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Calculus Questions
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...
find the power series representation for 1/(1-x)^2
Find the relative maximum value of f(x,y,z)=xyz2, subject to the constraint x+y+5z=6 The Relative Maximum value...
Find the Taylor series for f(x) centered at the given value of a. [Assume that f...
Complete four iterations of Newton’s Method for the function f(x)=x^3+2x+1 using initial guess x1= -.5
Given the function f(x) =cosh(x) with period of 2π , determine its Fourier series for interval...
The value of real estate in a city is increasing, without limitations, at a rate proportional...
1. A population of rabbits oscillates 21 above and below an average of 103 during the...
Find the general solution of the differential equation 10y' + 4y/x = 1/y^4
Find the area of the region enclosed by the curves y=x2+2x, y=x2-6x+8 and the line y=...
If z = x2 − xy + 4y2 and (x, y) changes from (2, −1) to...
Find the Taylor series for f(x) centered at the given value of a. [Assume that f...
Let ? = ? + 2? + 3? and ? = −4? + 6? + ??,...
A stone thrown vertically on Mars. Suppose a stone is thrown vertically upward from the edge...
Determine whether the Mean Value Theorem can be applied to ?(?) = ?^3 − 3? +...
A plane flying horizontally at an altitude of 1 mi and a speed of 470 mi/h...
Find the volume of the solid generated by revolving Ω about the indicated line. y=x^3 ,...
What does the Extreme Value Theorem say? Explain how to find the absolute extrema of a...
Differentiate the following fuctions. (a) y=arcsin(e^x) (b) f(x)=cosh x times 4^x (c) y= ln ((x-1)^2/(3x+1))
Given that the acceleration vector is a(t)=(-9 cos(3t))i+(-9 sin(3t))j+(-5t)k, the initial velocity is v(0)=i+k, and the...
Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval....
Slopes of tangent lines: Find the slope of the lines tangent to the following polar curve...
A car starts from a point at 2:00 p.m. and travels north at 40 mph. Another...
If z = x^2y − 6xy^2, find the following. (a) zxx = (b) zxy = (c)...
An outboard motor has an initial price of $1,920. A service contract costs $350 for the...
Find the present value of the income c (in dollars) over t1 years at the given...
The profit P (in thousands of dollars) for a company spending an amount s (in thousands...
If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the...
A projectile is fired at an angle of 28 degrees above the horizontal with an initial...
Explain why the following statements are true or false. a) If f(x) is continuous at x...
A bathroom scale is compressed 0.06 in. when a 180-lb person stands on it. Assuming that...
Find the angle between the planes 15x−25y+z=−18 and 9x+3y+19z=−6. Round to the nearest degree, and do...
How do I show whether sigma(n=1 to infinity) sqrt(n)/(1+n^2) converges or not?
For problem 1 to 3, use r(t)= <e^2t cost, e^2t sint, e^2t> to find each of...
For the function f(x)=2x3-18x2+48x+3, determine the following: a) Domain b)Intervals of increase or decrease c)Local max...
The weekly demand for DVDs manufactured by a certain media corporation is given by p =...
2y''-2y'-4y=2e^(3x) -Find W -Find u1' and u2' -Find General Solution
Sigma(1, infinity) (2^n x^n)/(n!) : Radius of convergence of this series?
A model for the surface area of a human body is given by S = 0.1096w0.425h0.725,...
3. Solve the following problem: The supply function for x units of a commodity is p...
A company has a plant in Portland and a plant in Baltimore. The firm is committed...
valuate SSSEz^2dV, where E is the solid region bounded below by the cone z=2sqr(x^2+y^2) and above...
it is known that W=x2y+y+xz where x=cos A, y=sin A, and z=A2. find DW/DA and calculate...
Homework #2 a) Find a vector perpendicular to the vectors 2i + 3j-k and 3i +...
Find the surface area of the portion of the sphere z = sqrt(4 - x^2 -...
Use the integration capabilities of a graphing utility to approximate the volume of the solid generated...
Find the directional derivative of the function at P in the direction of v. f(x, y)...
Given the function g(x) = x^4 – 5x, find the slope of the curve at the...
Introduction to differential equations 1. y' = x-1+xy-y 2. x^2 y' - yx^2 = y
Use the helix: r(t)= (bcost)i +(bsint)j +(ct)k , b>0 I only need e and f. I...
5. A new virtual festival called CovidPalooza is being planned for this summer and will take...
The population of Chicago in 1995 was 187,035. It had grown to 228,330 by 2005. Assuming...
) Solve the differential equation dydt= cos(t)y+sin(t) using either the method of variation of parameters or...
The function V(t)models the relationship between the volume of a tumor and the amount of time...
p is the price per unit in dollars and q is the number of units. If...
Find an equation of the tangent plane to the surface given parametrically by x = u^2,...
The Deligne Dam on the Cayley River is built so that the wall facing the water...
Find the general solution of y'' − 2y' = sin(5x) using the method of undetermined coefficients
f(c) = 1 / (c - 1) Demonstrate how it is one to one and show...
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for...
Find all values of x and y such that fx(x, y) = 0 and fy(x, y)...
Find the volume of the solid formed by rotating the region enclosed by x=0,x=1,y=0,y=4+x^6 about the...
Calculate the area of the surface bounded by y = x^3 and y = −2x^2 +...
3. A large box is made from a piece of cardboard that measures 10ft by 10ft...
A force of 8 lb is required to hold a spring stretched 2 in. beyond its...
For the next two equations, you will need to include derivatives of the nonhomogeneous term in...
Solve the following differential equations by using variation of parameters. y''-y'-2y=e3x
Using cylindrical coordinates, find the volume above the ??− plane and the cylinder ?2+?2=25 and below...
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