SECTION 6.2 VOLUMES I 387 efore, we have V = A(x) dx = T(x² – x*) dx %3D 6.2 Fined the of the solid enclosef ay the velume euclased 4=X,y=Vx aboutx=2 eurves. %3D

Q: 2) y In(y) dx + (1+x²) dy = 0

A: Given: ylnydx+(1+x2)dy=0⇒y lny dx = -(1+x2 ) dy⇒dx(1+x2) = -1ylnydylet lny =t

Q: Question 1 dy What is dx of 5/ - 25 = 1 ? dy 15 y/3 A dx 4x½ dy 4x½ dx 15 y½ dy 15 y½ 16

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Q: Exercise : Find dy O y = 1ox +3 Co sx Oy=cscxm4X+7 Catx 1+ Cotx

A: Note:- As per our guidelines, we'll answer the first three sub-parts of this problem. Please…

Q: Find the DE of y2 =Ax+B A. y' = VAx + B %3D B. yy" + (y')² = 0 C. 2yy" + (y')² = 0

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Q: 2 (Dx-2Dx0y +Oy)u= 3Xy %3D AMS. 4

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Q: 1 dy find 10 dx x=2. If y = dy = %3D dx x= 2 (Simplify your answer.)

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Q: (x'= -2x ly'= -2y Consider the dilation f(x,y)= a. Find the dilation factor of f. b. Find AA'B'C',…

A: Solution:   4.

Q: If u = x+ 1 t= vu y = t² then, 1. dy = 0 dx dy 2. = x dx dy 3. = 1 dx dy 4. = vx dx

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Q: 7 F Cx) = X tên?x 2\ %3D 2. X+ f'x)= %3D

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Q: Find dy/dx and d2y/dx2 of x= t + 1/t, y= t + 1

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Q: Let y= x +2X. Find dy when x = 3 and dx = 0.1. A 0.8 B) 6 0.1 D 8

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Q: If  z = 8x2 + y2  and  (x, y)  changes from  (1, 1)  to  (0.95, 0.9),  compare the values of Δz…

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Q: ven the bivariate data: 2. 3. 5 y 6. 8. 7. 1. Draw a scatter diagram for the data. 40 Grap 8 Afte…

A: Given data is X 1 2 3 5 6 y 9 8 7 3 1   Scatter diagram for the data is

Q: 3:30 A3. If y = e2x+5 then y' = %3D LA) 2e2x+5 (b) e2x+5 (c) 5e2x+5 (d) e2

A: Given query is to find the derivative of the expression.

Q: 2x dx x+x+7 S* r?e-3* dx

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Q: df at (1,2) If f(x,y) =tan' -1 Y then find O a. df dx 1 at (1,2)= 10 %3D O b. None O c. df -1 at…

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Q: Expand d/dx (Yx)

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Q: 1: find af/ox and af/ày.. ) (x, y) = Vx² + y²

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Q: -s Jatx? 3. 4-/ sinx coss dx |

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Q: Defnie x Sin ( fG.9) = %3D %3D is corfinugs al Co,0)

A: *** This is the problem related to Multivariate Calculus and we are advanced math expert and have…

Q: хе*+2 y = e2x+1

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Q: Find dy/d 5x²+xy+ N9 - Say %3D =D0

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Q: Use laplace tansform y"+ + 4y" +qy'+1Oy= - 24+e y1o) =0, yl0) = -4 , y"O) -1o %3D

A: We use Laplace Transform to find function in t

Q: ーy -x+x = 2 +X = o. %3D

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Q: Find dy/dt.

A: Find dydt.

Q: ay + 2y = 3 dx %3D dy + 4y = x³ - x dx dy .2

A: A first order linear differential equation is expressed by the form  dydx+Py=Q Here, P and Q are…

Q: 1-CAL182 y =Vx+4 29- y=x-2 SVx+4dx + [(Jx +4- (x – 2))dx → a = ?,6 = 2,c = ?,d = ? area = A) a- 4,…

A: Break the function into interval and find value of limit for each interval.

Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: Let f(t) = 2t², g(t) = ²tỉ, and h(t) = 4t. Compute [ Ver)² + (s(})* + (r(t))* dt Check your work as…

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Q: b) y = [ dx Integrate. 13 +5

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Q: et 5" f(x)dx = # and Sf(x)dx = . and Sf(x)dx =. Find So f(x)dx. 3n %3D

A: Given the integrals are: ∫02πfxdx=2π5 and ∫2ππfxdx=3π2 Find the value of ∫0πfxdx. Here we use adding…

Q: First order linear in (y-x+xycotx)dx+xdy=0

A: The given problem is to find the solution for the given first order linear differential equation.…

Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

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