7) Use Theorem 7.1.1 (Table) to find L{f (1)} for the following: S()=(e" -e")° а.

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A: Given,          ∫0π214-cosθdθ

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A: Here we need to use muller's methode.

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A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

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Q: Question 4. Reduce the equation Uxr + Uyy - 2uz + 4uy + u = 0 into the form Vrr + Vyy +cv = 0 =…

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Q: Question 1 π 2x Evaluate the integral cos(xy)dydx 4

A: ∫45∫0π2xcosxydydx

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A: The solution is given in the next steps below:

Q: Problem 1 in attached image

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Q: This question is designed to be answered without a calculator. If g(x) = si sint dt, then g'(x) = 0…

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Q: 1.4 Using the graph in Figure 1.7 below, find Saf (t)dt and if the area of the shaded region is A,…

A: Given the graph representing the area

Q: Question 12 If L{f (t) }= | e-(s+1)! ¡2sin²4 dt_then what is f (t)? ,- (s+1)! ¿2sin²t dt, then what…

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Q: Question 2 > The function ` f(x) = (5 x-9)e^(-6 x) ` has one critical number. Algebrically use the…

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Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

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A: This is a problem of Taylor and Maclaurin Series.

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Q: Question 9 19. Se3z tanh(e3) In cosh(e³²)dz a. 1/6 (In cosh (e"))² +c c. 1/3 (In cosh (e))² +c b.…

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Q: 2. In each of the following, find fyzz, fæyæ, fryz. 2. f(x, y, z) = ln(xyz) + z² tan-'(e=")

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Q: his question is designed to be answered without a calculator. = f(x) = 1-2e-x, then f has horizontal…

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Q: Question 1. Find the linearization of the function y = f(x) = x² sin(x) at a = T/4 and use it to…

A: Linearisation of f(X) at a is given by-  L(X) = f(a) + f'(a)(x-a)

Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

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Q: 4. g(t) = e³t + cos(6t) – e³ªcos(6t) 5. f(t) = tcosh(3t) 6. h(t) = t²sin(2t)

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Q: Example 2.13. Obtain graphically an approximate value of the root of x = sin x + T/2.

A: Please find step by step solution below

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Q: Question 2 Let r, y ERt with x < y. Show that y-l<x-1.

A: We have to prove that the given inequality.

Q: QUESTION 11 dz = = zP z1- -i (-e2 – 1)i e (e? + 1)i e (e? – 1) ei (e2 – 1)i e

A:

Q: 2. a) Determine the values of n and h required to approximate e2x sin 3x dx to with in 10-4 by the…

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Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: QUESTION 16 Let f(x) = sin(x) -e*, Po=0, and p, 1, then by Secant method P2 = 0.657614 0.678614…

A: Given that: f(x)=sinx-e-x,       p0=0 and p1=1

Q: QUESTION 2 Determine a potential function for F(x,y,z) = sin(y)e³²i - xsin(y)e?j + 3xcos(y)e32k or…

A:

Q: Question 8 Integrate the function. dx V9 - x2 COs:1 X+C 2 cos x+ sin x+C D sin *-C Question 9 413

A:

Q: QUESTION 1 Solve the following first order pde by the method of characteristics: du at du + X = 2xt…

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Q: 1 1. The function Y = sin(t² )+ 4 is graphed below. Define F(x) = [, sin(1²) + - 1 dt 4

A: Given: F(x)=∫0xsint2+14dtThus, Fx represents the area under the curve y=sint2+14(a) First of all we…

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A:

Q: Question 5 4x2 Calculate the integral: dx 5+ x² V5 + x² - 10 ln V5 2х + C (5 + x²) 32 V5 + x2 V5 2х…

A: Indefinite Integration

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A: We shall answer first three subparts as per the guidelines. You can post it again by mentioning…

Q: 1.4 Using the graph in Figure 1.7 below, find SLaf (t)dt and if the area of the shaded region is A,…

A:

Q: Question 11 Integrate f 9z2 - 5+dz Type only the numeric value below and be sure to show all of your…

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Q: QUESTION 4. Use the improved Euler method with h = 0.2 to approximate to 5 decimal places the…

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Q: Question 10 x²+x+1 Ja 2x²+2+x³+x So - dx = [Aƒ (x) – B ln(g(x)] + D fb dx, and if A = ,B<0, then…

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Q: Question 10 [i[cosh:(2x²) – sinh ( 2x³) ]dt is equal to A © Sude xdx E None

A: Integration

Q: Question 4. (3 marks) Verify if the function u(x, y) = sin(2x – y) is a solution of the following…

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Q: Question 16 d If g(x) = == S[e²-In (21+1) ]dt, find g(x). dx 4 A et + (2x+1)2 e* -In(2x+1) 4 e¹+ (2x…

A: We will first find g(x).