4. Test the existence and uniqueness of solutions of the initial value problem: dy 2xy y(-1) = 1 dx 4+x² + y²¹ on the rectangle R: x + 1 ≤ 1 & ly - 1 ≤ 2.

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Q: 4. Verify that (¹)² (j³)² = j³² | j³² but (²)³ #jj² j2

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Q: 9. Evaluate the following integrals: (Simplify your answers) (a.) [x¹² cos(x-6)]. X+3 8(x-4)dx -2x…

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Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

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Q: 3C. The diagram, act drawn to scale, shows two parallel line segments, MA ad RK, cut by two…

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Q: 2. Find the terminal point P (x, y) and the reference number determined by t=- Round the coordinates…

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Q: 3. Panera Bread estimated its yearly sales to be $588 million at the end of the year. Actual sales…

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Q: 3. Express the principal value of 1n z in rectangular form. a) z = -5 b) z = -2 + j2 c) z = √2 + j√6…

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Q: 19. Show that (for n = 0, 1, 2,..) (a) F(-n, b; c; 1) = (c-b)n (c)₁

A: We have to show F-n,b;c;1=c-bncn Solution: By Pochhammer definition cn=Γc+nΓ(c)           (1) and…

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Q: : Find a solution op of the I.V.P.: Y₁ = −y₁, y₂ = y₁ +ty₂, y(0) = []

A: To solve this problem using the following steps  First we find the particular solution of the first…

Q: D) Calculate the following definite integral: [* (/{√x - 1) dx

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Q: 2+13 H.W. Evaluate zdz along the following paths- 1+12 (a) horizontally from 1 + 12 to 2 + 12 then…

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Q: Prove that if r^n and q^n are solutions to the recurrence relation of the form a_n = αa_(n−1) +…

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Q: 2.Proof that any tangent plane for the surface F(- point = 0 passses through a fixed

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Q: 13 0 Problem3: Suppose M | 1 20 004 024 a = 2,B of (B) Әр - B₁ B₂ B3 (a) Let f(B)=B'MB-a'ß. Express…

A: It is given that M=130120004, a=024, and β=β1β2β3.

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

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Q: 11. Fill-in the box. Given: Rectangle ABCD with diagonals line MA and line RK R Proof: A M Prove:…

A: We need to prove MR ≅ AK

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Q: 5 Give an example of a sequence of continuous real-valued functions f₁, f2,... on [0, 1] and a…

A: It is not uniformly convergent.

Q: Which number is equivalent to ? 34 A B C D 2 9 81 729

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Q: Use the graph method to apprroximate the root of f(x) = x³ + 3x-5, and use the provided graph paper.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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Q: b) Graph the following trigonometric function for the interval 0 ≤x≤ 2: y=2 sin(x)

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Q: Intelligence as measured by IQ score = 136 is best described as O Nominal Ordinal O Interval O Ratio

A: To choose correct option for given question