which of the following polar equations represents a cardioid? -r= 3-2cose r= 4+4sin0 r= 2+3sine T =1-3cose

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A: Given the graph. Determine the sign of f(a), f'(a) and f"(a).

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A: Here we have to use the Runge-Kutta 4th order method

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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A: ∫ 16sin2xcos2xdx

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A: This question is based on application of diffrential equation.

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A: Topic:- sequence and series

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A: We want  to maximize the function.

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A: Determine the Laplace transforms

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Q: Q28- The value of e-(In+1 )n is a) (-1)" e--1 b) (-1)"e" c) (-1)" e-+1 d) (-1)" e-"

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A: Topic:- application of integration

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Q: 12 – r|, 2. Suppose f(r) = {0, if a > 2 if r = 2 14 – 22|, if r < 2. (a) Find lim f (x). z+2+ (b)…

A: a)limx→2+ f(x)=limx→2+ 2-x=limx→2+ 2-2 =0b)limx→2-  f(x)=limx→2- 4-x2=limx→2- 4-4 =0

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Q: If a = (-6, 12, -9), b = (2, -16, 18), and c = (28, -14, 3), what is %3D %3D (51, 0, -24) (57, -48,…

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Q: е. — 4t3 + 16t +9

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A: Follow the procedure given below.

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Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4.x + 2y + z subject to x +…

A: Apply Lagrange multiplier

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A: Vector

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A: a The given series: ∑n=1∞n3n3+4n+5

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A: Given v=2i+3j-6ku=5i+12jWe know that i.i=j.j=k.k=1i.j=j.k=k.i=0

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A: Given y′=(1+1/x)⋅y,y(1)=2.7183,h=0.2,

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A: here i am providing my hand written solution

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Q: Find the Laplace Transform of the given function using the definition of Laplace Transform a. f(t) =…

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Q: Directions: Read the problem carefully and answer the questions that follow. The population of a…

A: Topic:- exponential growth function

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A: Given query is to find function is continuous or not.

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A: To find the center, transverse axis, vertices, foci, and asymptotes. To grapg the…

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A: This question can be solved by the concept of nature of graphs.

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A: This is a problem related to calculus. Based on the available concept we will answer the question.…

Q: 13) y"+7y'+12y = 21e", y(0) = 3.5. y'(0) = -10.

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Q: The state of decay of radium is proportional to the amount present at any time. Suppose that 400 mg…

A: Here we will find radium left after 2.5 hours and 10hours,