Show that sin jx is orthogonal to sin kx in   C[ -π,π] for j ≠ k,j,   k >=1.

Q: Find the LU factorization of A = A = and use FORWARD SUBSTITUTION AND BACKWARD SUBSTITUTION to solve…

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Q: 2. CAUCHY SEQUENCES Fix a constant ≤K≤7. Let (n)-1 be a sequence such that x₁ = K and for all n 9…

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Q: Let || = 0 曲 -1 1 1 nd a pair of vectors u, v in Rª that span the set of all x € Rª that are mapped…

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Q: It follows that y = lim x+4 f(x) +8 x-4 7 is the equation of the tangent line to y = f(x) at the…

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Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy da y =…

A: Sol:- Substitute dydx with y' y' =5+18xxy2Rewrite in the form of a first order separable ODEy2y'…

Q: Use the figure to find each of the following. NOTE: If the limit does not exist, indicate that using…

A: Note: A limit tells us the value that a function approaches as that function's inputs get closer and…

Q: 6 -4 5 -3 7 6 1 -3

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Q: Let T: R² → R2 be the linear transformation which first reflects in R² about the line y = x, and…

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Q: (-10) " lon a. Center of convergence b. Radrus of convergence C. interval of convergence {- (x-5)

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Q: 2. Derive the Newton method for finding √2+√3. Then start with ro = 2, find 71,72. Write your answer…

A: First we find the equation having the same root as the given value. let  x=2+33   taking qube of…

Q: 2. Write the general term for each arithmetic sequence in simplified form. a.) ti-6 and d = 2 22…

A: Solution :- 2 Question a) t1=-6 and d = 2General term of arithemetic sequence is given as :-tn= a +…

Q: 20) a) Verify that both y₁= 2t - 1 and y₂ = t² are solutions to y' = 2(t-√√t²-y) In which intervals…

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Q: Q2.4 that satisfies the following determine a vector function conditions outlined below: r"(t) = 3…

A: We are given that        r"(t) = 3cos(5t) i + 8sin(6t) j + t6 k   So, integrating both sides, we get…

Q: VnEN 2 > 2n

A: According to guideline we need to solve only first question. If needed the rest of the question…

Q: 9+²2²-12x+10y+29=0 since it is, 3x-2y What is the value of the expression? A)-8 B)-6 C) 6 D) 8 E) 12

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Q: By letting u(x, y)= X(x)Y(y), apply the method of separation of variables on the partial…

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Q: Let z = f(x, y) = x² + y² be the temperature at a point (x, y) = R². (a) Draw a sketch indicating…

A: We know that the directional derivative of a function z=fx,y at a,b in a direction v→ is calculated…

Q: Find C, no,f(n) such that |T(n)| ≤ Cf(n)| whenever n > no. a. T(n) = n² + 10n + 10

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Q: Problem 9: Suppose V1, V2,...,Um is a linearly independent list in a real inner product space V.…

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Q: Prove that if G is a group with the property that the square of everyelement is the identity, then G…

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Q: 2. CAUCHY SEQUENCES Fix a constant ≤K≤7. Let (n)-1 be a sequence such that x₁ = K and for all n 9…

A: You are asking for part a) and part b) only so here it is,

Q: Corrent Attempt in Progress Compute A2-2A+I. 0 -5 '300' A = 0 0 2 NOTE: Write the elements of the…

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Q: 6. Find an inverse function for sinh(z) = 2 such that its value at 0 equals 0.

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Q: Problem 5: Let A € M2×2(R). For u, v € R², define fa(u, v) = ut Av. 1 Here we are taking u and v to…

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Q: 3.2 Exercises PS2.9 Consider the matrices: A = 2 0 4-5 2 B Compute each matrix sum or product if it…

A: The given matrices are A=20-14-52, B=7-511-4-3, C=1221 (g) We have to find AT+3BT. (h) C-3I2, where…

Q: . Consider the graph. (1.25) (2.33) (4.49) (3,41) (5, 57) (6.65) (7.73) (8,81)

A: To solve this problem, I will use the following fact:If a line passing through the pointsx1,y1 and…

Q: Solve c)

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Q: how many ways can a teacher give five different prizes to five of her 26 students?

A: I have written the answer with in the solution.  Please go through that.

Q: A survey asking mobile phone users how long they would wait for a page to load found the following…

A: Given that the data  Time (Seconds)           Percentage           < 1…

Q: 13) Hampus cycles to work early on a Wednesday morning. In order to make it to the lecture, he has…

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Q: Exercise 1: Mixed quantifiers Let f(x) = 1. Prove that the limit of f in 0 does not exist, i.e. that…

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Q: bra 2 A. A B. B C.C D. D 4. The graph represents the cost of a medical treatment, in dollars, as a…

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Q: (2.00-x) Vq₂ = ±xV|q₁|

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Q: Determine the set of points at which the function is continuous. x²y³ f(x, y) = 2x² + y² 1 if if…

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Q: Compute the pseudo inverse of A

A: The given matrix is A=1101 We have to find the pseudo inverse of matrix A.

Q: 6. Find the following limits using any methods: a. lim 24 b. lim +2

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Q: Solve number 1

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Q: 3. A person deposits $1000 in an account that yields 9% interest compounded annually. 3.a Set up a…

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Q: Test the paint and Find the solution differential equation: to the y² - xy + 2y = 0 at Xo =0

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Q: At some imaginary school, there are n students and m courses. Each student is free to enroll in…

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Q: Taylor Series. e the Taylor series for ln(x) centered at x = 1 to approxim = function f(x) = x ln(x)…

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Q: For each of the following functions, calculate the first- and second-order partial derivatives.…

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Q: A conservative vector field is given by F=(-z-1)i + (-2y+2)j + (-z-1) k. Select two options that…

A: I have written all the answers within the solution .please go through that.

Q: (d) Find the direction of the greatest decrease in temperature at the point (-2,1). What is the…

A: The directional derivative is said to be directional if the rate at which any function changes at…

Q: [12] The vector –4 is a linear combination of the vectors 11 matrix equation At = has a solution,…

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Q: 6. Use Newton's method to find solutions accurate to within 10 for the following problems. a. et + 2…

A: MATLAB CODE :- %solve nonlinear equations using newton raphson %x0 is the initial guess of the root…

Q: 29. Construct 3 x 2 matrices A and B such that Ax = 0 has only the trivial solution and Bx = 0 has a…

A: 29)

Q: [x=1-2t The point of intersection of the line y=2+t and the plane 3x-2y+z=14 is z = 3+2t (5, 0,-1)…

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Q: Test the convergence of the power series below: Calculate the following: a. Center of convergence b.…

A: Given, Test the convergence of the power series below: ∑n=1∞(-1)n10n(x-5)n We have to find the…

Q: Linearize f(x) = √2-x for a = 1 and use it to approximate the value of √1.5. L(x) = The approximated…

A: The given problem is to linearize the f(x) for a=1 and also to find the approximate value of √1.5…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.