Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z2 (3, 7, 2) 3V 62 7V 62 2 Vf(3, 7, 2) = 62 62 V 31 Find the maximum value of the directional derivative at the given point.

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Q: Consider a nonhomogeneous differential equation y" + 4y = -12x + 10e. (a) Verify that yp = -3x + 2e*…

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Q: V3 1) tan 3 cos¯1 –1 -1 2) cos-1 | 3) sin- 0 4) tan-' (-V3) 5) tan- 6) sin- 7) cos 2 8) tan- –1

A: tan-133

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Q: 1. (20) Solve IVP of the harmonic oscillator: dy dy dt2 + 4- + 6y = e-2", y (0) = 0, y' (0) = 1. dt

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A: Explanation of the answer is as follows

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A: This question can be solved using the concept of derivatives.

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A: We have to find the parametric equations.

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Q: [1] What is the c value of a parabola with a Vertex of (4,2) and a Focus of (4,4)?

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

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Q: Find the total area between y = 16 – x and the x-axis for 0 <x < 5. | Area

A: Please refer to the image below

Q: 6. Simplify each of the following using the properties of logarithms: (a) In () (b) log2(VE5) 8y3

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Q: A 2-ft-high and 5-ft-wide r

A: answer is in next step

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Q: 3. Find the area bounded on the right by x+y=2, and on the left by y=x and below by x-axis.

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Q: Use l'Hôpital's Rule to find the following limit. 5 sin (x) - 5x lim 2x3

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Q: 2 – 5n 11п-1 n=1

A: Use ratio test.

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Q: 3 п2-п-2 1. n=3

A: Given query is to find the limit of the expression.

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A: Volume of cone(V)=13πr2hr8=h22⇒r=4h11Substitute in the volume formulaV=13π×(4h11)2×h   V =16363πh3

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A: Solve using integration by parts.

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

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A: To find the equation of the plane passing through the point (-7,10,-3) and containing the line…

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A: We have to mention the general form of the particular solution

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A: Given cos(x)=35 and sin(x)&lt;0

Q: sa = -1, a = 0, and a = 2,c

A: answer is in next step

Q: Suppose that the graph below is the graph of f'(x), the derivative of f(x). Find the open intervals…

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Q: (-() Write the linear system in matrix form. Assume X = dx = x - y + z + t – 1 dt dy dt = 2x + y – z…

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Q: Find the area under the given curve over the indicated interval. Q 14- y= 2x [1, 6] ... The area…

A: Given: y=2x, (1,6)

Q: Use the table of values to find lower and upper estimates of r10 f(x) dx- Assume that f is a…

A: We have to find the upper an lower estomates.

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: sin 8 What is the exact value of Show your work for partial credit.

A: Find the value of sin(7pi/8).

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A: Solve

Q: Definite Integrals, Average Value (Homework) In a certain city the temperature (in °F) t hours…

A: In a certain city the temperature (in °F) t hours after 9 AM was modeled by the…

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