+ Assignment_1_sec07_spring21.pdf Problem 7. a. Find the local maximum or minimum value of the following function. Find the interval where the function is increasing and where it is decreasing? yA

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A: Given query is to find the solution of the differential equation.

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Q: 12. Find the gradient vector field, Vf, of f(x,y)=x?y+y°.

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A: Solving

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A: We have to determine the type and stability of the critical points of the homogeneous systems.

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Q: Convert the Cartesian coordinates (-2, 2/3) to polar coordinates. (4, 150°) (4, 120°) O (6, 120°)

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Q: dx Vx²+2x+5

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Q: Convert the Cartesian coordinates (1, 0) to polar coordinates. (1, 0°) (1, 90°) (0, 0°)

A: The cartesian coordinate is  x, y = 1, 0 To evaluate: The polar coordinate corresponding to the…

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A: The objective of the question is determine the Cartesian co-ordinates.

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Q: Sketch the curve y = x4 - 6x2 and show intercepts, maxima and minima and points of inflection

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Q: 10

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Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim, 3 f (x)=21 x→3 b) limx? -x+1=-5 c) lim x→2…

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Q: Determine the critical numbers of g(x): + 16x). %3D 0= x4 - 8x2 +16 ーx4 t8x2 +0 -16 =E (-, g(x) = x…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: 1. Determine the type and stability of the critical points of the homogeneous systems: dx (a) = x –…

A: Solving

Q: Show that the following are equal using set identities. Provide the correct solution with the name…

A: The left side is: C∩C-B∩C∪A∩B-B∩C-A We first simplify inner parts:  C-B∩C A∩B-B∩C

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Q: answer

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Q: Does this mean the sequence is always convergent?

A: We can take limit of the sequence.  limn→∞an=limn→∞-1n-1nn+n

Q: Convert the polar coordinates (2, 60) to Cartesian coordinates. (1, √3) (√2, √2) (√3, 1)

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Q: The polar coordinates expressed as Cartesian coordinates are |(1, O) (-1, 0) (0, 0) O (0, 1)

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