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Calculus Questions
1. Find the absolute maximum of f(x,y)=x^2+2y^2+4y-2 on the disk x^2+y^2<=4 2. Let E be the...
Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (1, 0, 0)...
Analyze and sketch the graph of the function f(x) = (x − 4)2/3 (a) Determine the...
Solve the initial value problem: y' = 7x3y y(0) = 7
Find the price that will maximize profit for the demand and cost functions, where p is...
How do you solve dy/dx=0.05-(y/43)*(7/60) when y(0)=0?
Solve the differential equation (3y^2+2ty)+(2ty+t^2)dy/dt=0
et S be the solid obtained by rotating the region bounded by the curves ?=sin(?2) and...
Suppose you have a function f(x) = -2x2 -4x +1 What is the horizontal and vertical...
A tank is filled with 10 gallons of brine in which is dissolved 5 lb of...
Solve the system of differential equations using laplace transformation dy/dt-x=0,dx/dt+y=1,x(0)=-1,y(0)=1
Given the region bounded by the function below and the x-axis on the interval also given:...
Suppose that f : [0; 1] ! R is increasing on [0; 1] and that 0...
Please graph these parametric equations please: x(t)=3-2cos3t, y(t)=1+4sin3t
Evaluate the Riemann sum for f(x)=0.4x−1.8sin(2x)f(x)=0.4x-1.8sin(2x) over the interval [0,2][0,2] using four subintervals, taking the sample...
A home improvement contractor is painting the walls and ceiling of a rectangular room. The volume...
Use Linear Approximation to estimate the increase in volume of a cube whose side increases from...
Consider the following. (If an answer does not exist, enter DNE.) f '(x) = x2 +...
An oil refinery is located on the north bank of a straight river that is 2...
Write the integral to show the area between the curves ?^2 − ? = 2 and...
A closed rectangular box is to be constructed with a base that is twice as long...
1) Use the First Derivative Test to find the local maximum and minimum values of the...
Find the Maclaurin series for x2sin(3x)
Design a rectangular milk carton box of width w, length l, and height h which holds...
The current toll for the use of a certain toll road is $1.50. A study conducted...
Find the absolute maximum and absolute minimum values of f on the given interval: x^4-8x^2+8 [-3,...
Find the absolute minimum of f(x,y)=x^2−y^2−x on the region R={(x,y)|3≤x≤5,2≤y≤4}. Express the answer as an ordered...
The region bounded by ?=2+sin?, ?=0, ?=0 and 2? is revolved about the ?y-axis. Find the...
Find where f(x) is increasing and decreasing f(x)= (x^2-4x-12)/x^2
Integrate using partial fractions (Lesson 8) 1. Evaluate Z 0 to 1 x/((x + 1)(x +...
Find the area of the region that lies INSIDE both curves r=5cos(theta) and r = 2...
13. You deposit $100 at the end of each quarter in an account that pays 6%...
Suppose you have a function f(x)= -2x2 -4x +1 What is the base function? What is...
After spawning Pacific salmon die so it is natural to measure the population size by year....
We have to build a box that has no top and whose base length is five...
A firms demand function for a good is given by P = 107-2Q and their total...
Let ? (x)= (x^2 -1)/ (3x-x^2) find the equation of the tangent line to the curve...
Find the exact global maximum and minimum values of the function g(x) = 3xe^-5x on the interval...
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer...
An open box is to be made from a rectangular piece of paper. The paper measures...
Use the shell method to find the volume of the solid generated by revolving the plane...
The vector ?⃗ is directed 30° clockwise off the positive y-axis with magnitude 2. Draw this...
Use synthetic division to factor the polynomial: f(x) = 2x4 + 7x3 + x2 − 7x...
Use a finite sum to estimate the area under the graph of the function f(x)=x^2-7 on...
If X does not occur free in Q, then ∀X(P(X) -> Q) is semantically equivalent with∃XP(X)...
(1 point) Evaluate the integral by reversing the order of integration. ∫3 0∫3 ? 24?^(3?^2)????
find the value of d2y/dx2 at t =π/4 if x=sint, y=tant
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 4. (A) Find...
Calculate two iterations of Newton's Method to approximate a zero of the function using the given...
Find the consumers' surplus at a price level of $7 for the price-demand equation p=D(x)=35−0.2x where...
*answer in detail, give example Suppose a given alternating series diverges. Can it converge absolutely? (yes...
A zoo supplier is building a glass-walled terrarium whose interior volume is to be 205.8 ft...
What is the third degree maclaurin polynomial for f(x) = 4^-x?
A tank contains 30 gallons of brine solution containing 10 lb of salt. Another brine solution...
the graph of the derivative Q' (x) is given below. We have Q'(0) =-2 (although it...
In each part below, sketch a graph of a function whose domain is [0, 4] that...
The formula E = 1000(100 - T) + 580(100 - T)2 is used to approximate the...
Apply the Laplace operator to the function ℎ(?,?,?)=?3xsin(−9?). ∇^2ℎ=
find the solution of y'' + 9y' = 1296 sin(9t) + 1134 cos(9t) with y(0)=4 and...
Consider the following. a1 = 8, an + 1 = 9 − an Calculate, to four...
The research department for a company that manufactures clock radios found they can sell1500 radios at...
The weekly demand function for x units of a product sold by only one firm is...
Use multiplication or division of power series to find the first three nonzero terms in the...
Given the function f(x) = x3 - 3x2 - 9x + 10 Find the intervals where...
suppose and are functions that are differentiable at x=0 and that f(1)=2, f'(1)=-1, g(1)=-2, and g'(1)=3....
3. Let ?(?) be the revenue in dollars from selling ? units. If ?(200) = 540...
The brain mass of a fetus can be estimated using the total mass of the fetus...
2. (a) Determine all first and second order partial derivatives of f(x,y,z) = x2y3 sin(xz) (b)...
Please show all work neatly, thanks. Find a set of parametric equations for the line passing...
Gloria would like to construct a box with volume of exactly 35ft^3 using only metal and...
Suppose you have a function of the general form e(x) = ax^3 + bx^2 + cx...
Practice Derivatives and integrals. A particle’s velocity is described by the function v = ( t^2...
The following is true: If f is a polynomial, then f is continuous. Which of the...
A 13ft. ladder is sliding down the wall at the rate of 7 ft/sec. Find the...
For each vector field F~ (x, y) = hP(x, y), Q(x, y)i, find a function f(x,...
Solve the initial value problem. f '(x) = cos(x) + sec2(x), f (PI/4)=7+((sqrt2)/2) f(x) = _______
Find a power series representation for the function. f(x)=x^3/(x-8)^2 f(x)=SIGMA n=0 to infinity Determine the radius...
The cost function for a product is C(x)=0.5x2+110x+170. Find average cost over [0,200].
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = 1/2x^(4) −...
How to know when to use the ratio, root, alternating, comparison etc... test when trying to...
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