Vx2 – 64 if x <-8 15. f (x) = {x+ 8 if – 8< x < 8; [-8,8] O if x > 8

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

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Q: Activity 1. Solve for what is asked. dy 1 1 1. Find :+= = 8 dx y 2. Find : x²y2 – 2xy = 8 dx 3. Find...

A: Differentiate with respect to x.  According to guidelines we solve only first three parts. 

Q: Find the length of the arc of the curve 9y? 4x3 from the origin to the point (3,2v3).

A: Here, the given curve is: 9y2=4x3⇒y2=4x39⇒y=23x32 Now, the length of the curve on [a,b] is given by:...

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Q: Solve for the derivative of the following and simplify if possible. h(t) = t3 - t2 sin t

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Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y...

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Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –...

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Q: Express the sum using summation notation. Use 1 as the lower limit of summation and i for the index ...

A: This question is based on summation problem.

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Q: Find the area bounded by y = sin?(x) and y = sin³ (x) from -<x<n.

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Q: /9-4х2 dx

A: We know, (i) ∫dxx2-a2=12alogx-ax+a+C, C is a constant.

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Q: 的+十」 (8-9) = TT

A: To evaluate the given integral.

Q: Find the particular solution of the differential equation that satisfies the initial condition. f'(x...

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

Q: V- 2 dx +1)

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Q: 8. On a warm day, the temperature of a room is 23°C. A biological sample is taken from cold storage ...

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Q: 12 Find the area under the curve y = over the interval [ – 1, 1]. (x + 2)² area = i

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-2ax=0x+y=2a

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Q: A farmer builds a rectangular grid of pens with 1 row and 5 columns using 550 feet of fencing. What ...

A: Given problem:- A farmer builds a rectangular grid of pens with 1 row and 5 columns using 550 feet o...

Q: (Q.2) Describe how to use the weighted residual method (2-term polynomial approximation) and write d...

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Q: 3 dx V9 – x2

A: We know that, ∫dxa2-x2=sin-1xa+C   ∫03dx9-x2=∫03dx32-x2                    =sin-1x3+C Now applying t...

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Q: Original Integral Rewrite Integrate Simplify dx 9. X + C dx

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A: Prove the identity cosh(x)+sinh(x)=ex

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotated ...

A: This question can be solved by first plotting the graphs to get the feel of the area enclosed.

Q: -3 (x + y)dx dy

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Q: 4. y+= y в. C. -y-4 D. y-4 с. А. 4y-2 4y-2 5. 4x2 + 4y2 = 36 A. - в. с. - D. 2 6. x2 + 3xy- y = 7 2x...

A: solution:-implicit differentiation(4)y+x2=y2dy+dx2=2y dydx2=2y dy-dy=2y-1dydydx=122y-1=14y-2option(B...

Q: Question 10 Find the area bounded by y = sin²(x) and y = sin³(x) from 0 < x<. %3D

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Q: Consider the parallelepiped with adjacent edges u = 5i + 5j + k v = i+j+ 8k w = i+ 5j + 7k Find the ...

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Q: Express the integral in terms of the variable u, but do not evaluate it. eS-4 dz; u = 5z – 4 NOTE: E...

A: ∫01 e5x-4dx  here change the variable x to u u = 5x -4 du/dx = 5 dx =du/5 limit is change from  if x...

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

Q: 2.

A: ∫x2ex dxBy integration by parts

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A: Here we have to integrate the given integral

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Q: Activity 6: Find the first and the second derivative of the following: 1. у 3D е cos x 2. y = sin³ (...

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for y...

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A: Just take the derivative of given function and get the required solution.

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