h. Let a rectangular plate R = [0,7] × [0, T/2] have a temperature distribution T = 200 sin(x) cos(y) °C. What is the average temperature of the plate? (Ans: 81.06°C)

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A:

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A: Average value of any function is ratio of  difference in outputs and the difference between inputs.

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A: The average rate of change of the function is:

Q: find the average rate of change of the function over the given interval or intervals.

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Q: 5. Find the following derivatives: a) y = x?e-2/x b) y = t tan -t- t -Int

A: Given:  5)a) y=x2e-2xb) y=ttan-1t-12lnt To find: Derivatives of the given functon.

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A: Since you have asked multiple questions in single request so we will be answering only first…

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A: (a) Given: +

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A: Find the average rate of change of f from 0 to π2 .     f(x)=cos(2x)

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A: Given x cosπxy=x+y+1

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A: We have to find

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A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

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A: Given: x=cos3θ and y=sin3θ To find: The derivative dydx

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A: Given: -

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A: The displacement of a particle moving back and forth along a straight line is given by the following…

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A: Using derivatives.

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A: Then plug this in the slope of the tangent formula

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A: Please refer to the image below.

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A: using , average rate of change…

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Q: 24) Find dy /dx for the following functions : a) y². cotx= [sin(x,y)]-¹ b) y = (lnx + x) tan x

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