1.) Find volume generated by the area bounded by y = 2x² and x-axis. You need to show two methods. y = x ³ about of solving this problem.

Q: 3. Show that (a) 8(-x) = 8(x), a<0<b 8(r)8(y) (b) 8(ax+by)8(cx + dy): = lad-bel

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Q: Find a formula in terms of k for the following determinant - -3-4-6 det -1 8-9-0 k -1 3

A: We have to find a formula in terms of k for the following determinant:

Q: An engineer wishes to design a trapezoidal gutter. The gutter is to be made from a strip of tin by…

A: From the diagram,  BEAE=sinθBE=asinθ and, CF=BE=asinθ and, ABAE=cosθAB=acosθ Now, area…

Q: 2. Can the problem below modify into an ill-structured problem? Or is this problem already included…

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Q: 3 Use Newton's method to approximate a root of the equation 5x + 7x + 2 = 0 as follows. Let 31 2 be…

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Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

A: To Evaluate: ∫C1z3(z-1)2dz where C is |z-3|=7

Q: points and determine whethe ons: -2xy + 2y² - 6x + 8x - 3y² + 24y + 7

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Q: u. vE=

A: Given as, E={u:o,T→ℝn u is absolutely continuous. u(0)=u(T).u∈L2o,T,,ℝN}˙

Q: Add the following Mayan numerals together. Make any necessary exchanges and show all steps. It's a…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: For the Maclaurin series expansion of sin(x) starting with the simplest term x^1/1!, add terms one…

A: Given Maclaurin series of sin(x) sin(x)=x11!-x33!+x55!-x77!+.... exact value of sinx at x=π4 is…

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

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Q: z+1 f(z) = fcdz z³+3z where C is the circle |z| = 1

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Q: 7.4 Lemma Let X be a normed space over K, and ƒ be a nonzero linear functional on X. If E is an open…

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Q: Solve the given initial value problem. 3|5_3|5 dx dy dt = 5x + y; = − 3x + y; - x(0)=2 y(0)=0 The…

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Q: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

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Q: Evaluate: ffefdxdydz

A: Given integral as∫01∫eez∫1yezxy dx dy dz

Q: Determine the singular points of the given differential equation. Classify each singular point as…

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Q: Evaluate: S 2y+3 (y-1)(³-1) dy ° − In\y − 1| − § (y − 1)³ + ¼ln|y² + y +1| - O √3 ○ – In|₁¹|- (y −…

A: We will use partial fraction decomposition to solve the given integral .

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

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Q: Maximise the profit for a firm, assuming Q > 0, given that: • its demand function is P = 4,000 - 33Q…

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Q: Consider the following function. f(x) = x/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a…

A: Given  fx=x67, a=1, n=3, 0.8≤x≤1.2

Q: Solve the given initial value problem. y''-10y' +25y = 0; y(0) = -5, y'(0) = 122 5

A: Sol:- y'' -10y' +25y=0A second order linear, homogeneous ODE has the form of   ay''+by'+cy=0For an…

Q: Let O(2, R) be the set of 2 x 2 orthogonal matrices. Describe all of the O(2, R)-conjugacy classes.

A: It is given that O2,ℝ be the set of 2×2 orthogonal matrices.  O2,ℝ-conjugacy class=X-1OX, where O is…

Q: Determine the cube roots of = (1+j3)(2-j)

A: Given complex number is z=(1+3i)(2-i)                     (1) taking log of both side lnz=(2-i)…

Q: a. Find all relations from { a , b , c } to { u , v }. b. Find all functions from { a , b , c } to {…

A: We have to answer the following questions :  (a) Find all the relations from {a, b, c} to {u, v}.…

Q: Use Cauchy's Integral Formula and Cauchy's Integral Formula for Derivatives, when appropriate, to…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 5, -3, -2), (-2, -3, 2, -3), (1, 3, -2,…

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Q: g(x) = 7 sinx, [0, π], 6 rectangles

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Q: Find a partner (friend or family member) and test your absolute threshold for sugar. Have your…

A: Given: An experiment to determine personal absolute threshold for sugar.   To determine: Personal…

Q: Determine the inverse Laplace transform of the following using the convolution theorem: 4 s²(S-2)

A: We use convolution theorem.

Q: 1. Consider the two functions f(x) = cos 4x and g(x) = { ) (a) Write down: (i) the minimum value of…

A: As per company guidelines we are allowed to solve one question at a time so i am solving fist one…

Q: Refer to the equations below: 4x + Ay = 4 Ax+y = −2 Find the value of A such that the system of…

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Q: 6. = f(z)=(-1+i)z-2+3i D = {ze C|Rez≥1}, where w= E

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Q: Evaluate √1 + x² dx dy ○ 2/3 ○ 2√2 3 O −1+2√2 3 O 1/3 8

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Q: Find a basis for the subspace of R³ spanned by S. S = {(1, 5, 7), (-1, 6, 7), (2, 6, 1)}

A: Write the given set of elements as the rows  to form a 3x3 matrix. The space spanned by the rows of…

Q: Next question The auxiliary equation for the given differential equation has complex roots. Find a…

A: We will use the following concept

Q: Add the following single level Mayan numerals together. Make any necessary exchanges and show all…

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Q: Consider

A: We use Definition of Compactness.

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0).  For this we use the proper…

Q: Which of the following is a valid triple integral? of sh() sh() f(x, y, z) dzdydr Jg(z) Jg(y,z)…

A: To find- Which of the following is a valid triple integral? ∫ab∫gzhz∫gy, zhy, zfx, y, z dz dy dx…

Q: Solve the initial value problem for t> -1 with y(0) = 16. Put the problem in standard form. Then…

A: We are given first order linear differential equation to solve this first we will write the problem…

Q: 1) Given R = 715, M= {0, 5, 10}, then R/M is 2) Given R = 7₁2 , M= {0,4,8} " then R/M is

A: Given :(1)  R=ℤ15 ,                M = 0, 5,10  =5ℤ          2  R =ℤ12                  M =0 ,4 ,8…

Q: A linear programming problem shows an objective function of: P = 250x + 75y Subject to constraints:…

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Q: Evaluate: S ○ (2-√2) T 8 ○ (2-√2) T 4 O (√2-2) T 4 O (√2-2) T 8 -y² sin √²+y² dady x² + y²

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Q: function C gives the number of bushels of corn produced on a tract of farmland that is treated with…

A: C is the number of bushels of corn produced . C91 can not be negative since the smallest amount of…

Q: Evaluate: ₁ da 2√x+3 ○1-3 ln (7/5) O2-3 In (7/5) 2 O2+3 ln7 03-In ()

A: Solution: To Find: ∫14dx2x+3

Q: Consider the differential equation: y" + y = sinx Solve it using all three methods that we learned…

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Q: Given the following matrices A and B, find an invertible matrix LI such that UA = B: You can resize…

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Q: For some of money to double itself in 5 years, what must be the rate of interest converted…

A: Let the initial principal amount  =P after five years amount A=2P time =5 years n=6 (bimonthly)…

Q: Find a unit vector with the same direction as the given vector . Use the square root symbol where…

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