A symmetrical trapezoidal plate has the following dimensions: The width of the parallel sides are, respectively, 2.5 and 4.5 ft. The perpendicular distance between those sides is 1.5 ft. The plate is submerged in a liquid in a vertical position with the parallel sides horizontal and the shorter parallel side at the tip and exact
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Let g be continuous on the real interval [0,1] and define H(z) := integral (from 0 to 1) [g(t)/(1-z[t^2])]dt, (|z| < 1) Prove that H is analytic in the open disk |z| < 1.
Please see the attached file for the fully formatted problem involving the cosine function related to integration by parts. A_n = l_-1^0 cos n pi t + l_0^1 t cos n pi t dt = 1/n pi [sin n pi t]^n_-1 + 1 / n pi [t sing n pi t]^1_0 - 1/npi l_0^1 sin n pi t dt = 0 + 0 + 1/(n^2pi^2)[cos n pi t]_0^1 = { 0 if n is even, - 2/(n^
Find the area of the region bounded between two given curves by integration. {(x,y): Y^2 ≤ 4x, 4x^2 + 4y^2 ≤9}
9. The temperature distribution u(x, t) in a 2-m long brass rod is governed by the problem ...... (a) Determine the solution for u(x, t). (b) Compute the temperature at the midpoint of the rod at the end of 1 hour. (c) Compute the time it will take for the temperature at that point to diminish to 5° C. (d) Compute the ti
A) (e^x/((e^x+2)^(1/2))dx between 0.5,0 b) (x^2/((1-2x^3)^(1/2))dx c) (sin^5(x))dx between ((3.14/2),0) d) (x^2 cos(x))dx e) (1/((2x+5)(1-3x)))dx f) (3x-4/((x-2)(x+1))) dx between the limits 5,4 g) (4x.e^(-4x))dx between the limits 1,0 h) (3x.sin(3x))dx i) (sin(4x) - 4cos(3x)
Please see attached. Hi, I am having trouble doing these problems listed below. Please show me how to solve these problems for future reference. Thank you very much. I would like for you to show me all of your work/calculations and the correct answer to each problem. For Exercise 2, find the mode of the probability
I am looking for the solution of this transformation I need a detailed solution. Also I would like to see the original formula for the Laplace transformations needed. If f(t) is a periodic, continuous function with period T>0, show that its Laplace transform is... Please see attached.
Without evaluating the integral show that (see attachment) when C is the same arc as the one in Example 1 (see attachment for example) Please see the attached file for the fully formatted problems.
1. Suppose f: [a,b]  is a function such that f(x)=0 for every x (a,b]. a) Let  > 0. Choose n   such that a + 1/n < b and |f(a)|/n <. Let P ={a, a+1/n, b}  ([a,b]). Compute (f,P) - (f,P) and show that is less than . b) Prove
1. Suppose f: [a,b]  is a function such that f(x)=0 for every x (a,b]. a) Let  > 0. Choose n   such that a + 1/n < b and |f(a)|/n <. Let P ={a, a+1/n, b}  ([a,b]). Compute (f,P) - (f,P) and show that is less than . b) Prove
(1) Find the volume of the solid bounded by the paraboloid x2 + y2 = 2z, the plane z = 0 and the cylinder x2 + y2 = 9. (2) Find the volume of the region in the first octant bounded by x + 2y + 3z = 6. (3) Find the area of the solid that is bounded by the cylinders x2+z2 = r2 and y2+z2 = r2. (4) Find the volume enclosed by t
(1) Find ... (x + y)2 dx dy...where R is the square with vertices (±1, 0) and (0,±1), (2) Let R now be the triangular region in the xy plane with vertices (1, 0), (2, 1), (3, 0). Find.... (3) Change the integral .... from rectangular to polar coordinates. See the attached file.
Showing that a particular differential form is closed but not exact, as an application of Stokes' theorem (differential forms version)
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A) Find the indefinite integrals of the following functions. Please see attached questions, please can you show your working to help me understand. thanks
Revenue at day D = (200 + 10D - 100P)*P D refers to the day, with Monday being 1, Tuesday 2, etc up to Friday with a value of 5. The assignment is as follows: 1. If you are charging $1 per cup, what is your revenue for each of the five days? What is your total revenue for the week? 2. What is the indefinite integral
7) Use Stoke's Theorem to evaluate curl F*dS S is the hemisphere oriented in the direction of the positive x-axis. 8) Use Stokes Theorem to evaluate C is the boundary of the part of the plane 2x + y + 2z = 2 in the first octant. 9) Suppose that f(x,y,z)= , where g is a function of one variable such that g(2) = -
Evaluate the line integral by two methods: (a) directly and (b) using Green's Theorem. ∫c xdx + ydy. C consists of the line segments from (0,1) to (0,0)...and the parabola y = 1 -x^2.... Use Green's theorem to evaluate the line intgral along the positively oriented curve. ∫c sin y dx + x cos y dy
1. Find the indefinite integrals for the following functions: a. f(X) = 10000 b. f(X) = 20X c. f(X) = 1- X2 d. f(X) = 5X + X-1 e. f(X) = 12- 2X f. f(X) = X3 + X4 g. f(X) = 200X - X2 + X100 2. Find the definite integral for the following functions: a. f(X) = 67 over the interval [0,1] b.
Differentiate the folloiwng with respect to the variables shown: Please see the attached file for the fully formatted problems.
B. Determine the path traced out by w as z moves along a straight line joining A(2 + j0) and B(0 + j2) using the transformation w = z^2. Please see the attached file for the fully formatted problem.
Calculus Integral Calculus(XIII) Definite Integral as the Limit of a sum Method of Summation
Evaluate the definite integral: Integral (b - a) 1/(x^2)dx, where the lower limit is a and the upper limit is b.
Calculus Integral Calculus(IX) Definite Integral as the Limit of a sum Method of Summation
A particle of mass 10kg, moving in a straight line, starts at rest from a point A under the action of a force that decreases uniformly from 20N to zero in 20 secs. It then travels with a constant speed for a further 20s, and finally moves under the action of an opposing force of 40N until it comes to rest at B. Find the maximum
Calculus Integral Calculus(VII) Definite Integral as the Limit of a sum Method of Summation Defin
Calculus Integral Calculus(III) Definite Integral as the Limit of a Sum Method of Summation Definite Integral It is an explanation for finding the integral by the method of summation or by evaluating the integral as limit of a sum (part 3). Find by the method of summation the value of: ∫ sin xdx, where the lo
Calculus Integral Calculus(II) Definite Integral as the Limit of a sum Method of Summation