To prove that: n²= 5k or 5k+1 or 5k+4 we use the following method: Division into cases. We need 3 cases We only need algebra to prove the given statement The statement is incorrect. Proof is not needed. Division into cases. We need 5 cases

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Q: Establish the identity 2 2 cos - sin 0 2, 1 - tan 0 2 = cos 0.

A: To establish the identity

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A: We will find the required.

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Q: 29. xy dx + 2(x² + 2y2) dy = 0; when x = 0, y = 1.

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Q: M

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Q: cos Ꮎ 1 + tan 0 sin Ꮎ 1 + cote = cos 0 sin 0 Suppo pat bus to as to

A: Left side is given by :cosθ1+tanθ-sinθ1+cotθ

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A: Differenciate function at given point and use equation of tangent plane

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A: Answer: As per guidelines we can solve only 1 question at one time so post other question separately…

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Q: Establish the identity. csc u cot u = sin u 1 + cos u

A: We have to establish the identity csc u - cot u = sin u1 + cos u.

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Q: Find the 9 9th roots of 12-13i

A: 12-13i = re-iθr=122+132=313θ=tan-11312=-47.28

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A: Answer: As per guidelines we can do only one question at one time , the solution is given below:

Q: Find the transform of the given functions by use of the table. f(t)= cos 3t-sin 3t

A: Lcos3t-sin3t=Lcos3t-Lsin3tUse Laplace Transform table:          Lcosat=ss2+a2,…

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Q: Write the sum as a product: sin(16.76) + sin(12.96) = > Next Question

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Q: Consider the function f(x) = = a) b) c) 4x²-7x-3 x²+6x-16 State the domain of f(x) using interval…

A: I have solved step by step in detail.....go through the solution

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A: The given functions, i) fx=5x2e3x+5ii) fx=ln x7x+23iii) gx=2x3-9x-2+7x5

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Q: 3. Let R be the region between the functions y = x² and y = 8 - x². Set up the iterated double…

A: Use the given curve and intersecting points to draw the region and iterated integral.

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Q: (85) 6-4,3) Graph off -10 (5,0) fo (8-2) Let f be a differentiable function defined on [-10, 10]…

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Q: Find the indefinite integral of Jsec²x tanx√1 + tanx dx. 22/2

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Q: Summarize the Fundamental Theorem of Calculus (FTC), Part II using your own words

A: We  have to write the meaning of fundamental theorem of calculus.

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then the integral L{f(t)}…

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A: Topic:- application of integration

Q: (1.1.1-4-3-3-4-6,...} 1, 3, 2, 4, 3, 5, 4, 6, { {

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Q: Given the function f(x) = x²-3x-4 x-2 Calculate: a) Intervals where the function increases and…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given: x=y4,y=1, and y-axis x=4