Let R be the region bounded by the functions f (x) = 2: 4 and g(x) = 4x as shown in the diagram below. Find the area of the region R using a calculator, rounding to the nearest thousandth. 13 12 11 10 9. 8 6. 4 2. R -1.5 -0.5 -1 1.5 -1 0.5 1. 2.5 3-5 -2 -3 -6 3.

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A: I am attaching image so that you understand each and every step.

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A: We have to find average value of given peace wise function.

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A: Please refer to the solution which is uploaded in step 2

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A: f(x)=xDerivative formula:f'(x)=limh→0 f(x+h)-f(x)hf'(x)=limh→0 (x+h)-(x)hf'(x)=limh→0 hhf'(x)=1ddxf(...

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A: The equation of the line is x-43=y+75=z+5

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A: I am attaching image so that you understand each and every step.

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A: Given query is to find the value of g(2).

Q: a.) z= 5.

A: We will find the second derivative of the given function in the following step.

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A: We will find the directional derivative. 

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A: Given problem:-

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A: We can find the integration as below

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A: a) fx=8e2xb) gx=9x5e-1 x

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A: Solution :∫cos6xcos3xdxNote :2cosacosb=cosa+b+cosa-b12∫2cos6xcos3xdx12∫cos6x+3x+cos6x-3xdx12∫cos9x+c...

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A: Given query is to find the deri at given point.

Q: -2 +5

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A: I have stated the used formulas in the solution

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A: topic- application of derivatives

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A: Let's find. 

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A: Select a normal vector and a point then write the equation of the plane. 

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A: We can solve the differential equation as below

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