1. Find the Fourier series for a periodic function with period 27 defined by f(x) = x,-π < x < π

Q: Evaluate the surface integral - [[F-ds when I = F(x, y, z)= e(4xi+j) and S is the graph of shown in…

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Q: The coordinates of the region is given in inches as indicated in the figure. Calculate the area of…

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Q: Write the system of equations -5x - 4y + 2z = 0 -4x + 5y + 12 = −4 -4 4x + 4y - 5z = 2 as a matrix…

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Q: Find the distance between the two vectors. 5) u (-3, 6), v = (6, -6) =

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Q: If P 1,500,000 borrowed at an annual interest rate of 8% has to be repaid in 15 months, find the…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: ✓3.14 Let p be the orthogonal projection of VE Rn onto a subspace S. Show that p is the point in the…

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Q: Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: (4) (a) State the fundamental theorem of cyclic groups. (b) State the fundamental theorem of finite…

A: In first we State the statment of fundamental theorem of cyclic groups. Secondly we State that  the…

Q: Two different questions have the same answer? And the answer is wrong

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Q: (b) Let {an} be the sequence defined by an = (¹ + ² ) ". (i) Show that {an} is an increasing…

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Q: Sketch the graph of the function below, including correct signs, x- intercepts and y-intercepts.…

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Q: ✓3.12 Find the orthogonal projection of the vector into the subspace. «()·()) » (²) 2 S = [{2

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Q: Use the method of matched asymptotic expansions to find the leading order uniform approximation…

A: Given equation ε y" - y' + (y2) = 1, we need to use the method of matched asymptotic expansions to…

Q: Complete the first three lines of an amortization schedule for the following loan. Assume monthly…

A: We will use Excel to solve this. Writing in tabular form:

Q: 5. There exists no integers j, k for which 18j + 6k = 1.

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Q: 3. Use the Ratio Test to determine if the following series converges. 3n n5.5n Σn=1

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Q: Construct a simple graph with vertices T, U, V, W, X, Y whose degrees are 2, 2, 1, 1, 2, 2 What is…

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Q: 1. Define F(x) = f(t) dt, where f(t) is given by the graph below. Find F(12) – F 6 4 3 2 1 Y 1 2 3 4…

A: A graph of a real-valued function is given. One must find the said functional value. It requires the…

Q: P= = D Let If possible, find an invertible matrix P so that D = P-¹AP is a diagonal matrix. If it is…

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Q: Catherine Dohanyos plans to retire in 20 years. She will make 20 years of monthly contributions to…

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Q: Problem 44. Use the Cayley-Hamilton theorem to compute the inverse of 12 1 A = 0 2 3 00-1

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Q: Q-1) Let be Euler Phi function. Calculate Þ(156), Þ(1800), Þ(588)?

A: According to guidelines we can do only first question thank you. Please repost 2nd question

Q: Find the image of the horizontal line y = 5 under the reciprocal mapping w = 1/z on the extended…

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Q: The operations manager of a large production plant would like to estimate the mean amount of time a…

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Q: 1. f: Z-Z decide whether has a right inverse or a left and exhibit these inverses if f has. (1)…

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Q: Find the value of an investment of $10,000 for 12 years at an annual interest rate of 3.15% The…

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Q: Suppose a man invested $250 at the end of 1900 in each of three funds that tracked the averages of…

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Q: 4.35 When we decompose a vector space as a direct sum, the dimensions of the subspaces add to the…

A: When we decompose a vector space as a direct sum, the dimensions of the subspaces add to the…

Q: Let f [-100, 100] → R be the function defined by x + 2 √x²+1 f(x) = Show that f has a maximum value…

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Q: 2. d²y(t) dt² + 6 dy(t) dt + 8y(t) = 5. sin (3t)

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Q: A professor records the following final grades in one course. Construct a frequency table for the…

A: We know that The frequency is the number of times the event happened in an experiment.  The relative…

Q: 4. Let y = [3] orthogonal and u = to u. 3 Write y as a sum of a vector in Span{u} and a vector

A: We shall solve first question only as you have asked more than one question as per the company…

Q: 9.15 Show limn→∞n! an = 0 for all a ER.

A: Our objective is below:

Q: Find the 1.7) using 4-term Lagrange interpolation For

A: The solution is given by

Q: Q-4) Let C₁, C2,..., Cn be real numbers. Prove that at least one of these real numbers is greater…

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Q: Determine which pairs of vectors in Exercises 15-18 are orthogonal. 8 -2 a= [ $; } b = [ 3³ ] -3 15.

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Q: || Let || A -1 0 01 30 0 2 1 possible, find an invertible matrix P so that D = P-¹AP is a diagonal…

A: Eigenvalues and Eigenvectors

Q: Question 2 Using an appropriate coordinate change, evaluate √² + y² + z²e(2²+²³+2³)² dV₁ where W =…

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Q: ideal. Show that is a prime ideal in Z[x]., but it is not a meaximal

A: Let R be a commutative ring and I an ideal of R. (i) I is prime &lt;==&gt; R/I is an integral…

Q: determine if series is convergence conditionally or divergent. state your reasoning make sure you…

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Q: Find the distance between x = 10 -3 and y = ㅗ -5

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Q: 3. (a) Let an max{sin 1, sin 2, sin 3,... sin n} Does {an} converge? What is its limit? Explain. =

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Q: 5. The temperature adjusted for wind chill is a temperature which tells you how cold it feels, as a…

A: Temperatures adjusted for wind chill at fixed wind speed of 20mph: Temperature at °F Adjusted…

Q: Let f(x)= 3x for every x E R. Let p(x) be the polynomial of degree at most two that agrees with this…

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Q: Find the solution of the simultaneous equations by Laplace transform with initial condition y(0) =…

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Q: solve this, follow the format below x³ +3.12x² - 13.64 = 0 (1 − 2)

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Q: Find the point on the sphere x²+y²+z²=5184 that is farthest from the point (-8,9,-15). ( )

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Q: A number leaves remainder 6 when divided by 10. What is the remainder when the number is divied by…

A: Given that, a number leaves remainder 6 when divided by 10. We have to find the remainder when the…

Q: If f(x) = 3x5 - x + 3, then what is the remainder when f(x) is divided by x-2?

A: We have to find remainder when f(x) is divided by x-2 We will use result that when polynomial f(x)…