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Calculus Questions
Let C be the hexagon in 3-space with corners at (−2,0,3), (−1,−5,3), (1,−5,3), (2,0,3), (1, 5,...
Which of the following are critical numbers of the function f(x)=x4−2x2+5 ?
Find the number of solutions of the following DE for various all real values of b>0:...
The marginal cost, in dollars per unit, for a company's portable heater is C'(q) = 48...
What are the dimensions of the lightest open-top right circular cylindrical can that will hold a...
Find the volume of the solid of revolution formed by rotating the area under the graph...
Find the slope of the tangent line to the cuve sqrt(7x+y) + sqrt(3xy) = 11 at...
The temperature on the surface of the sphere x^2+y^2+z^2=9 is given by T(x,y,z)=2x+2y+z, What is the...
Suppose f(5) = 2 and f′(5) = −0.5. Estimate f(6).
At which point does the function f(x) = 96xex3+7x−1 have a horizontal tangent line? (A) (−1.16667,...
Find y' and y'' for x2 + 6xy − 5y2 = 4.
1.) Find the equation of the tangent line to the graph of the function f(x)=5x-4/2x+2 at...
Logarithmic differentiation to differentiate: y = 3x^(3x)
Write the partial fraction decomposition of the following rational expression. (x^2-5x+12)/(x-5)(x-2)(x+1)
Find f. f '''(x) = cos(x), f(0) = 1, f '(0) = 3, f ''(0) = 7 f(x) =...
1) Explain how sequences are used to find the sum of an infinite series 2) Explain...
rewrite the geometric series 1/8+2/80+4/800+8/8000+.....with summation notation and determine if it converges or diverges if the...
7. A rectangular storage container with an open top is to have a volume of 10...
calculate lim (x-0) (e^x-1)/sinx
A company has a plant in Scranton and a plant in Salt Lake City. The firm...
What type of polynomial is the golden state bridge in San Francisco?
Brand Z's annual sales are affected by the sales of related products X and Y as...
Find an equation of the tangent to the curve at the given point by both eliminating...
Find the Laplace transform F(s) = ℒ{ f (t)} of the function f (t) = (7...
Consider the region in the xy-plane bounded by the curves y = 3√x, x = 4...
Find the directions in which the function increases and decreases most rapidly at p0.Then find the...
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer...
1.) Use the second derivative test to find the relative extrema for f(x) = x4 –...
Find the general solution of the following differential equation. Primes denote derivatives with respect to x....
Let the function f be defined as f(x) = x 2 − x + 30, where...
consider the funtion f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2 a) Find the domain of f. (write...
Vehicle A is headed due west from a fixed point PP at a rate of 4545...
Let D be the region enclosed by the cone z =x2 + y2 between the planes...
The complex has 250 available living spaces. Our monthly profit in dollars is modeled by the...
Consider the function on the interval (0, 2π). f(x) = sin(x)/ 2 + (cos(x))2 (a) Find...
1 C. A reservoir in the shape of a straight circular cone is filled with water....
Jared throws a penny off the top of a building that is 240 feet tall. The...
find the area of y=x^2 -6x +8 y= 2x-7
Use Lagrange Multipliers to find the maximum and minimum values for ?(?, ?) = ?2? given...
The general solution of the system of coupled equations d x d t = 2 x...
Please show all work to the problem. Thanks! The problem is to find the solution to...
Be sure to highlight the step (illustrated below) in your answer sheet, when using the chain,...
1. For each value below, enter the number correct to four decimal places. Suppose an arrow...
Differentiate the function. s(t) = 2t − 4(2t^4 + 2)^3 Find the indicated derivative. dz/dx for...
The velocity function of a particle is given by v(t) = 3t2 – 24t + 36....
Use Taylor Series to estimate the value of ln(3.4) knowing that the value of ln(1)=0 ,Perform...
After a large number of drinks, a person has a blood-alcohol level of 200 mg/dL (milligrams...
Use the Theorem of Pappus to find the volume of the given solid. The solid obtained...
An aquarium that holds 40 cubic meters of water is to be made such that the...
a) Find the equation of the tangent line to f(x) = e –x at the point...
A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a)...
The demand function for a certain commodity at a sales price of p dollars follows the...
Use the definite integral to find the area between the x-axis and f(x) over the indicated...
Find the minimum sum of two positive numbers (not necessarily integers) whose product is 600. pls...
the demand function P=1600-4q is for trucks (p=price q=quantity) Average cost= (300/q)+20 is my TC=300+20q since...
Find the eigenvalues and eigenvectors of a 3x3 matrix. (Create a question and solve this step...
Find the exact area of the surface obtained by rotating the curve about the x axis....
Each unit of a product can be made on either machine A or machine B. The...
Find the derivative of w=4ck^2q. Assume c and k are constants.
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a...
A function is given by h(k)=∫∞0xke−xdx. Its values may be found in tables. Make the change...
Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per...
Find the present value of the income c (in dollars) over t1 years at the given...
x2y′′ − 20xy′ + 110y = 280/x find the general solution
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a...
Suppose that 6 J of work is needed to stretch a spring from its natural length...
1) Set up, but do not evaluate, an integral to find the volume when the region...
Find dy/dx by implicit differentiation. x^2 + 7xy + y^2 = 12
find the indefinite integral. 1.) elongated S dx/x(lnx^8)^9 2.) elongated S 1/x^8/9(3+x^1/9) dx 3.) elongated S...
what values of x would you use to calculate a right rectangular approximation of function on...
Investigate function f(x)= x3+px+q for maxima and minima. Study also monotonicity intervals, convexity/concavity regions and inflection...
State whether each of the following functions are continuous or not for all values in their...
Define strength and work. How do you calculate the force made by moving an object a...
A tank has the shape of a hemisphere (bottom half of the sphere) with radius 6m....
A box with a square base and an open top must have a volume of 864...
Set up an integral to find the volume of solid obtained by rotating about the given...
Determine the degree of the MacLaurin polynomial for the function f(x) = sin x required for...
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. 3. z=x/y, x=se^t, y=1+se^-t 4. z=e^rcos θ,...
Find the volume of the solid formed by rotating the region enclosed by y=e^2x +5 ,...
Find the coordinates of the center, the foci, and the vertices of the ellipse with equation...
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