The graph of f is shown. y y = fix) 10 10 20 30 40 Evaluate each integral by interpreting it in terms of areas. 10 (a) f(x) dx 25 (b) f(x) dx 35 (c) f(x) dx

Q: dy 80. VI + x dx xay + x. %3D

A: Given: 1+x3dydx=x2y+x2

Q: Use the product rule to help you find dy/dx for each of the following functions: 13. y = (x²)(2x -…

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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: Differentiate the following functions: 6. y = csc-(2sinx)

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Q: A 27. Describe the geometric meaning of the double integral of a function of two variables.

A: To Describe the geometric meaning of the double integral of a function of two variables

Q: 1. f(x)=x²+2x+1 & f(x) = 2x+5

A: To find the area between the curve.

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² - c² and y = c² - x² is…

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Q: Integrate the following. 3. f sec?x dx tanx

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Q: Differentiate the following function: y=6x' +5x -4x+2

A: Differentiate of the function

Q: c) Consider the following two functions are given: y = 2x - x² and y = x². i. Sketch the two curves…

A:

Q: y =9-x? 2y = x² -3x +12 13. Find the area bounded by these two curves: and

A: Given: y=9-x2 2y=x2-3x+12

Q: 6. Fill in the blank: The length of the graph of y = x² on [2, 4] is equal to the area under the…

A: y=x2 on the interval 2, 4. Differentiating with respect to x, we get dydx=2x Now length of the curve…

Q: ۱۴ 14 g 3 3+1x 1= x² + 1× AND -FIND /dx WHEN X=2 =6.

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Q: 2. Find the area enclosed between the curves y =x² +2x +11 and y =-4x+2.

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Q: y = (cos x)* 4. Differentiate the function

A: Given :  The function  y = ( cos x ) x    To find :  The derivative of   y = ( cos x ) x

Q: –1 dx

A: Solve the following

Q: Determine the area below f(x) = 18-2x and above the line y=8+x. Sketch the graphs.

A: