Let be a measurable space and let be two -finite measures defined on . Suppose and is the Radon-Nikodym derivative of with respect to . Define by Show that is a well-defined linear isometry and is an isomorphism if and only if (i.e are mutually absolutely continuous). ---
I am not sure how to set up this problem, I think that I have to use the exponential rule, but after that I am lost. (See attached file for full problem description with complete equations) --- The quantity q, of a certain skateboard sold depends on the selling price, p, in dollars, so, we write q = f(p). You are give
1).Thermal Inversion When there is a thermal inversion layer over a city (as happens often in Los Angeles), pollutants cannot rise vertically but are trapped below the layer and must disperse horizontally. Assume that a factory smokestack begins emitting a pollutant at 8 AM. Assume that the pollutant disperses horizontally, form
Find the derivative of a) y=cuberoot(4x^2-sqrt(cotx)) this is referring to cuberoot of entire function b)ln(x^2)+(ln x)^2-ln(e^x^2)+e^x^2
Find the derivative of the following functions g(x)= ln(x-2/e^x-2) h(x)=tan^3(2x)/sin^3(2x)
A). Let M be the set of functions defined on [0,1] that have a continuous derivative there ( one-sided derivatives at the endpoints). Let p(x,y) = max_[0,1]|x'(t) - y'(t)|. 1).Show that ( M,p) fails to be a metric space. 2). Let p(x,y) = |x(0) - y(0)| + max_[0,1]|x'(t) - y'(t)|. Is (M,p) now a metric space? Please
For this equation E= (-C/r) + D(-r/P) (Where c, D, and P are constants) Do the following procedure: 1. Differentiate E with respect to r and set the resulting expression equal to zero. 2. Solve for r0 in terms of C, D and P. Here is where I am at in the problem: I have obtained a derivative (and I'm look
Find the first derivative of problem in attached file. It is only one problem. Find the 1st derivative of f(x) = (e^x + e^-x)/x
Prob. 2. The area of a rectangle (x,y) is the product xy. The perimeter of a rectangle P is 2x+2y. For a given P, find x and y that gives the largest area of a rectangle (x,y) for given perimeter P. Hint: Maximize A(x) = xy, where y = (P-2x)/2. Prob. 3. Find the 1st derivative of f(x) = [(3 - x^(2/3))][(x^(2/3) + 2)^(1/2
Question 1 says to differentiate using the quotient rule f(x) = 1 + 2x/1-2x where x < 1/2. My answer is -8xsquared/1 - 2x squared.(at x = 1/4) Question 2 says rewrite the expression of f(x) = ln (1 + 2x/1 - 2x) (-1/2 <x<1/2) by applying a rule of logarithm and then differentiate. So rewriting f (x) = ln (1 + 2x) - (1 - 2x) =
I cannot use mathematical symbols. Thus, I will let * denote a partial derivative. For example, u*x means the partial derivative of u with respect to x. Moreover, I will further simplify things by letting p=u*x and q=u*y. Also, ^ denotes a power (for example, x^2 means x squared) and / denotes division. This is the problem: T
Please see attached problem using quotient and composite rule.
Can you help to graph and find the antiderivative and the derivative. (See attached file for full problem description)
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Find a function f(x) such that f''(x) = x^2 + cos x and f(0) = 1 and f'(0) = 0. --- Please see the attached file for the fully formatted problems.
Let: v(t) = { 2t 0< t < 5 {10 5< t < 10 be the velocity of a particle given in meters per second. Find the distance traveled by the particle from t = 0 to t = 10 seconds. --- Please see the attached file for the fully formatted problems.
X^2y^2-2x=3 I'm trying to verify my answer for the first derivative, and see if I got the second one right as well. For the first derivative I got (1-xy^2)/(x^2y) I think I'm having a problem with the 2nd derivative because I got x^2-2x^3y^2+x^3y^4 It doesn't look right to me,
1. Express the function in the form f(x) = a(x-h)2 + K and indicate the vertex. a. f(x) = -x^2 + 13x - 8 b. f(x) = 4x^2 - 8x + 1 2. An object is thrown upward from the top of a 160-foot (Ho) building with an initial velocity (Vo) of 48 feet per second. How long after the object is projected upward will it strike the ground?
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Let f(x) = e sin x - cos x How are all the values of x E [-2pi, 2pi] found, such that a tangent line to the curve is horizontal and what are they? Please see the attached file for the fully formatted problems.
A tank holding 1000 gallons is being drained. The volume in the tank is given by: V (t) = 1000 (1- _t_)^2 for 0 < t < 40 40 where t is given in minutes. Find the rate at which water is draining from the tank. When is the tank draining fastest? Please see the attached file for th
Use inverse functions and implicit differentiation to prove that: d (tan^-1x) = 1___ dx 1+ x^2
Use the Product rule for radicals to simplify each expression. Please see the attached file for the fully formatted problems.
At noon, ship A is 100 km west of ship B. A is sailing south at 35 km/h and B is sailing north at 25 km/h. How fast is the distance between the ships changing at 16:00 h?
Find the derivative (with respect to x) for each of the following. Do not simplify. (1) x2y3 = sqrt(2x 5) + sin(8y + 3) (2) f(x) =((8x + 3)/2x^2 3)^5 (3) y = 4th root of ((1 3x)^4 + x^4). See the attached file.
Use the definition of the derivative to find the slope of the tangent line to the graph of f(x) = 1/(3x -2) at x = 1. See the attached file.
Find two numbers whose sum is 10 and product is as large as possible.
See the attached files. C(q) = 0.000002q^3 - o.o117q^2 + 84.446q + 23879 R(q) = -0.00003 * q^3 +0.0495q^2 + 118.02q P(q) = -0.000032q^3 + 0.0612q^2 + 33.554q - 23879 Use the Cost, Revenue, and Profit functions to find. a) C`(q) b) R`(q) c) P`(q) Do these equations predict the quantity needed to maximize profit, and th
Question 1 A bucket-shaped container has a circular base of radius 10 cm, and its slant height is 30 cm. the radius of the open circular top of the container is 10x cm. the curved surface of the container is modeled by part of a cone, as shown below. Please see attached.
Please could you solve this question clearly showing every stage used in getting to the answer. Differentiate the following expression with respect to θ... please see attached.