Inter secting the sphere x*az²4 with the peleme z-L results in two surfaces. Make a roughelon. Let s be the smallest of the two suskaces (sellecf the smallest in area without proot.). Caleuda te the flow of the vector field F (sy.2) = -2,2, x) leaving the surface S( to outside tne sphere).

Q: ) Find the antiderivative of each function. (a) f(x) = 4/2_1 (b) g(x) = 3e + sec? (c) h(x) = 8 sin x…

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Q: da find the 2-24 Series

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Q: Find one real root of g (x) = ln(x*) = 0.70 between 1 and 2. How many number of iterations were…

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Q: Question 2: Consider the nonlinear system -x1 + 10x2 - cos(x -x2) - 2 = 0 10x, + x2 + sin (x, + x2)…

A: We will use fixed point iteration method to find the function G, which will have its equilibrium…

Q: O Forthe Bernstein falynominte prove that こニ-x)()c-x) ヒニ。 6 prove tht the set A=, cosser gaCosnx isk…

A: 6. The Euler's formula can be stated as follows: eax=cosx+isinx

Q: Let us expand f(x) = x, 0<r < 1 in the series f (a)-ΣΑ, J, (μεα) , k=1 where denotes the kth zero of…

A: Given : fx=x3 , 0&lt;x&lt;1 We have to expand fx in Fourier-Bessel series           fx=∑k=1∞AkJ3μkx…

Q: а), J: Find the length of the curve y=3/7 x, 0<x<3 Length= ]: Find the area of the surface b)…

A: Let us consider the function y=f(x)  The length of the curve in the interval [a, b] is obtained as…

Q: is solved by New e initial guess of iterations would

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Q: Which quadratic function has the largest maximum? (1) h(x)= (3- x)(2+x) (3) k(x) =-5x² -12.x +4 (2)…

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Q: Find T(0)

A: Introduction: The tangent vector of a vector valued function rt is represented as r't. The necessary…

Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

A: We can solve this using newton backward difference formula

Q: xInx at 0<x<1 1-X Show that the function f(x)= is integrable on the interval [0,1]. at x = 0 -1 at…

A: The problem is from Theory of Integration.

Q: (4D4 - 4D3 - 3D2 - 2D + 1)y = 0

A: We have to solve the given equation.

Q: A lease valued at $22,000 requires payments of $1,629 at the beginning of every three months. If…

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Q: Q3) Use the Newton-Raphson method to find the root of f(x) = -0.5x *(4 – x) – 2 with initial guess…

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Q: 15. Evaluate SLL:(z+1)dV where E is the solid enclosed by the paraboloid y = x2 + z² and the plane y…

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Q: Determine the effective annual yield for $1 invested for 1 year at 4% compounded quarterly. O A.…

A: Annual effective yield

Q: Question 1 Given the double integral I (*- 3)dA where where D D= {(x,y)| 0sys/16-x²} a) Sketch the…

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Q: The natural numbers are N= {1,2,3,..}. The prime numbers are P = {2,3,5,7...}. True or false? ØSN…

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Q: A model for the height h (in feet) of a Ferris wheel car is h = 70 + 70 sin(4at), where t is the…

A: Given that   h=70 +70 sin(4(pi)t)

Q: Find the radius of convergence, R, of the series. Σ n2x 6 12 18· (6n) ... n = 1 Find the interval,…

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Q: Make sure that a) The set {vi, v3 with vi = (2,9) and v = (1, 1) iş a base of R2 b)The set {vi, v3,…

A: We have to check the following : a) The set v1, v2  with  v1 = (2, 9)  and  v2 = (1, 1) is a base of…

Q: Find the first two iteration of Jacobi method for the following linear system with x=(0,0,0) 10x, -…

A: Given linear system 10x1-x2=8-x1+10x2-2x3=5-2x2+10x3=8

Q: Use Mathematical Induction to show that 512|8 · 5" + 6 · 32n – 80n – 14 for all n E N.

A: We have to show that 512|8⋅5n+6⋅32n−80n−14 by using principal of mathematical induction. Let…

Q: Solve the following system 2x1 – 6x2 – x3 = -38 -3x1 – x2 + 7x3 = 34 -8x1 + x2 – 2x3 = 20 | using…

A: Coefficient matrix not diagonal

Q: Let P(R) be the space of polynomials of degree at most 2 and p(x), q(x) E P2(R) where p(a)-2, q(r) =…

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Q: 4. Find the solution of the following set of simultaneous equations by LT with conditions y(0) =…

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Q: . Let S be the part of the sphere r + y +z2 = 4 located above the plane z = 0, oriented at the point…

A: Here we can use divergence theorem to find the flux. Theorem states that If S is a closed surface…

Q: Qs: Solve the fallowing differential equation a) X y?y'= x*4 2yH

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Q: Al is at the point (0,6) and Bob is at the point (8,0). They are both running towards the origin. Al…

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Q: use Euter me thed to solve y's 2-24

A: Let us consider the given function y'=f(x,y), y(x0)=y0 Solving using the Euler method  Then the…

Q: Which sets are proper subsets of set A? A = {1, 3, 5, 7, 9} Select all that apply. O {1, 2, 3, 4}…

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Q: 9. Use the method of undetermined coefficients to solve the given system -4 X + 4t +9e X' %3D

A: To find- Use the method of undetermined coefficients to solve the given system X' = 1-441X + 4t +…

Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

Q: nd Solve:- Qz: Chssify - 3x dy +(3メ+リ』 = e

A: Given differential equation is xdydx+3x+1y=e−3x. Simplify it, we get dydx+3+1xy=e−3xx Now, the…

Q: Q) find Fourier series on [0,21] (3) ƒ(x)=cos x = COS X

A: find the fourier series on0,2π fx=cosx fourier series is given by…

Q: Without solving the exact answer, calculate sin(2) by evaluating up to six terms of Maclaurin series…

A: For the solution follow the next step.

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

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Q: (r' x r") r" Ir' x r"|2 Find the curvature and torsion (1 = | of the curve x = 3 sinh(t), y = 3…

A: Given that x=3 sinht, y=3 cosht, z=3t So r→t=x=3 sinht+3 cosht+3t

Q: 2. Find Inverse Laplace transform for the following functions: s + 7 s2 – 6s + 8 a) F(s)

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Q: Find the Bernstein Poly nomial when You put n =5. that means want to find Ba (f(x)

A: Berstein polynomial for a real valued function f on interval [0, 1] is defined as…

Q: (c) 4 h(x) = 8 sin a + 1+x? (d) f(1) = 5 cos I -

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Q: 4 For what value(s) of x is the function f(x) 2x? - 6х NOT continuous? A. x = 0 and x = 3 B. x = 3…

A: To find- For what value(s) of x is the function fx = 42x2 - 6x NOT continuous? x = 0 and x = 3 x =…

Q: , Find the antiderivati 4x3/2 –1

A: Introduction: We know that the antiderivative of some functions is as follows:…

Q: Round-off intermediate values to 7 decimal places, and 5 decimal places for the final answer. Find…

A: According to bisection method to get root of f(x) =0  Find two points a and b such that f(a) .f(b)…

Q: Q2/ Complete the following table to find the values a, b,c and s y -1 2845 308 3162 1 3544 a 2 3992…

A: We will have to fill the given table using newton's divided difference method.

Q: Sumi Kato's savings account has a balance of $1292. After 12 years what will the amount of interest…

A: Compound interest formula

Q: find ĕ = 1tiG residues Re12) Satis fies the equation

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Q: Give an enumeration procedure for the set L = {ab*a™: n> 1, m >1}.

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Q: Determine whether the relation ? on the set of all people is reflexive, symmetric,  antisymmetric,…

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