Find the total area of the shaded regions. 2 y=x√ 25-x -8 -6 -4-2 Ay 25 20- 15- 10- 5- 15 -10 -15 -20 -25 2 4 6 do 00 ▪▪▪ The total area of the shaded regions is. (Simplify your answer.)

Q: Laplace Transforms. 1. Determine the Laplace Transform of the following functions: a. f(t) = 5te-t +…

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Q: 2).  Draw the directional field for the differential equation. y' = 1 − y2 − x2

A: Given  y'=1-y2-x2

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A: Given,  y=1-x, y=0, x=-3

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A: solution is given below

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A: The function is given as , fx,y=lnxy+x2 find the directional derivative at point -1,1 in the…

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A: To find the derivative of the following functions

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A: Average Rate of change for the function f(x) on a,b is f(b)-f(a)b-a .

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A: From the graph of the function, we have to find its increasing and decreasing intervals.

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A: Solve the given

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A: We have to apply Rolle's theorem.

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A: Solution: y=32x2 vertex = (0,0)

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Q: with

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A: This question can be solved using the concepts of differentiation.

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A: We have to find the value of N.

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A: Please refer to the image below

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A: Please refer to the image below

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Q: answer #2 using partial fractions

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

Q: True

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A: We can find the inflection point as below.

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A: The objective is to find the solution of the above question.

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A: The region is bounded by the curves y=ex, y=x2-1, x=-1 and x=1

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