3. Consider the functions_f(x)=(x-a)(x−b), g(x)=(x−p)(x−q)_and_h(x)= g(x) If a‡b‡p‡q, then a) which two functions have the same set of zeros? b) does h(x) have any asymptote(s)? What is/are the vertical asymptotes of h(x) if that exists?

Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

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A: This is a problem of system of differential equation.

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Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

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A: Differentiating given function below

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A: The solution is given as

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A: The given series is                                     ∑n=0∞-1n64n-2n! We know that    ex=∑n=0∞xnn!

Q: 6. In the figure, AB // CD. The straight line EF cuts AB and CD at G and H respectively. Find x.…

A: Given: In the figure below AB|| CD. The straight line EF cuts AB and CD at G and H respectively. To…

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A:

Q: 9. Laplace Transform of f(t) = 1, 0 2. O A. 1/s + e^(-2s)/s + e^(2s)/s^2, s>0 OB. 1/s + e^(2s)/s +…

A:

Q: Ju udv-uv- 1 [vdu to Explain why the substitutions below are inappropriate. Let dv <=x x dx 1.…

A: Here we will find how to use integration by parts

Q: or n>3

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A: Solutions

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A: We will write v as linear combination of u1 and u2 and then find values of

Q: 8 d. Sex 0 dx

A:

Q: 3.) Evaluate ff cos(x-y) sin(x+y)dA, where R is the triangle with R vertices (0,0), (-л,π), and (,)…

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Q: (a) Let f: R 11 k=1 R be a function given by f(x1,x2,...,xn) = x²₁x²...x2, where 1. Show that the…

A: As per our guidelines we are supposed to answer only one question. Here first question answered.

Q: Use Romberg integration to compute R3,3 for the following integral S²x x³ cos x dx

A: Given integration is I=∫01x3cosx dx For n=1 sub interval h=1-01=1 Then by Romberg  method…

Q: (b) Show that the function defined by IN if (x, y) (0,0), √√√z²+y² f(x, y) = 0 if (x, y) = (0,0) is…

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Q: 4. Use power series to find two linearly independent solutions of this differential equation (x -…

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Q: 4. Where N denotes the set of natural numbers, say that a set X of natural numbers is computably…

A: The solution to this question is indeed, An is calculably divisible from B. This is on the grounds…

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A: Solution : Given, y"+cos(x)y=0 Let Expanded form of y is , y=∑n=0∞Cnxn y'=∑n=1∞Cnnxn-1…

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Q: Given the system below, 3x₁x₂2x3 = 7 X1 + 7x2-3x3 = -19 x₁2x₂ + 10x3 = 71 Use the following method…

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A: We have to solve given problems:

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A:

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A: Solution : Market 1 : The number of customers will increase by 800 each year. Market 2 : The number…

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A: Since  you have posted a multiple  question according to guildlines I will solve first  (Q2)…

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Q: (a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + 22 +1 + +…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Using the Laplace transform and showing the details of your work, solve the IVP: 8. y₁= -2y+3y2, y2…

A:

Q: Q2: Use Linear Least-Squares Regression to fit the following variables: Xi 1 2 3 4 5 6 7 8 9 10 yi…

A: Given

Q: ) = x² + y² - 8x - 6y subject to the

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A: given :- f(x) ={ 0                 for   -π≤x&lt;0,            {sinx          for     0≤x≤π.   a)…

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A:

Q: Let ƒ : f: R” → R be a function given by ƒ(x1,x2,...,xn) = x².x² …x², where n x² = 1. Show that the…

A:

Q: 2) Perform the following index shifts: i. Write y = no anx" as a series that starts at n = 2 ii.…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: CORRELATION ANALYSIS Determine the relationship between the number of hours students spent per week…

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A: We have to find the number of acres of wheat and barley to maximize the farmer's profit.

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Q: Let T:P2 →M be defined by T(p(t))=[p(1) p(1) p(1) p(1) p(1) p(1)], where P2 ={at2 +bt+c,where a,b…

A: Given : T : P2 → M  defined by ;   Tp(t) = p(1)p(1)p(1)p(1)p(1)p(1) ,  where  P2 = at2+bt+c : a, b,…

Q: 2) t (y-1) dt +y(t+1)dly=0 31 хчуу! -2y =. 41 yan- x lnn dy ==

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Q: 1. Suppose £5000 is invested for five years. Calculate the amount accumulated at the end of five…

A: As per the guidelines i had solved the first questions kindly post another questions separately.