3- A box with an open top is to be constructed from a square piece of cardboard, 3m wide , by cutting out a square piece from each of the four corners and bending up the sides. Find the largest volume of such a box

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A: Infinite gp

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Q: find the y a) y= CtX_ メ

A: As per guidelines we have to solve one question Please repost other questions again

Q: If Ax) = Vx -1 and g(x) = x+ 1, which expression is equal to fAg(x))? 1+ー1 Wx²+2x (x + 1) - 1 ベズ+x-1

A: Solution:

Q: The technique used to prove that x4 - 2x + 2/2tan-1 3 X + C 2. dx = - - x² + 2 is Long (Euclidean)…

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Q: 22. Sketch the region bounded by f(x) = Vx -1 and g (x)=x-1 AND find the area.

A: Sketch

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A: The equation of of tangent to a curve f(x,y)=0 at a,b is (y-b)=dydx(a,b)(x-a)

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Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: Rewrite the following equation in logarithmic form and use that to solve for the variable. Show all…

A: To solve for x

Q: sin x cos x -dx (2 sin x – 1)(sin x + 1)

A: To solve: ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Let I = ∫sin⁡xcos⁡x(2sin⁡x−1)(sin⁡x+1)dx Substitute sinx…

Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

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A: We need to find second derivative.

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A: Please see the below picture for detailed solution.

Q: 1. Find r(9/2)=? 2. В (3, 2) %3D?

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Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y = 0, a regular singular point is: X=4 x=2…

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Q: Ssec10dE

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Q: 8- Consider u=x², v=1/u+1 and w=vv find dv/dx

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Q: a. Determine the point (a, la)) for which f'(a) = a, given that Ax) = -x + 3x-7. b. Write the…

A: For (a), Given: We need to find the point a for which f'(a)=a. Here, f'(x)=-2x+3. So,…

Q: Determine whether the series is absolutely convergent, conditionally convergent or divergent. Please…

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Q: 4 Find f(x) dx if if x< 2 f(x) if x 2 2.

A: To evaluate the given integral

Q: Using appropriate trigonometric substitution, dx xV4 – x2 is transformed to J csc 0 de cos e do the…

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Q: convergent or divergent. Please provide detailed solution. a) : E 10" n=1 (n + 1) 52n + 1 00 -5n 2n…

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Q: 3. y = Vx and y = x3 y%3D

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Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: 5. For which values of a and b the following function is continuous at x=-2 3x + a x -2

A: A function f(x) is said to be continuous at a point x=a iff limx→a-f(x)=limx→af(x)=limx→a+f(x)…

Q: The following telescoping series 1 sin-1 sin -1 n + 1 n=1 converges to 3 converges to= the above the…

A: Given problem:-

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: Q3/ Find the limits x*+x²-2 1. lim X-1 -1 Vx+2-1 2. lim X-1 x+1

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Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: 1 The resulting 8. 6. The graph of y = log, x is horizontally stretched about the y axis by a factor…

A: Given , a graph y=log2x x is horizontally stretched about y axis by factor of 18 we need to find the…

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Q: y = log, x+1

A: Given: y=logx-1x+1

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Q: L,x²(x³ + 8)²dx 19. Use the Fundamental Theorem of Calculus to evaluate:

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Q: 3 y = Vx and y = x³

A: We have to find the area by using definite integral

Q: In how many ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table? 24 12 20

A: We have to tell number of ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table…

Q: dz dz IV. Suppose z is a function of r and y, and tan Vy? +x² = z*e®%. Solve for and fie

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Q: Evaluate 3x- 2y ds where C is the line segment from (3,6)to(1,-1)ts -58.240 58.240 O -57.991 O Non…

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Q: x*dy tly' txy) (y+xy)dx =0 3-

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Part 3: Integrate the following Show your complete solution. 1.) f (x + 5x -x)dx 3.) S 12x(7+ 6x*)dx…

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Q: 26 Select the correct answer. Which matrix can be multiplied to the left of a vector matrix to get a…

A: The given problem is solved below in detail.

Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

A: Given:  xy3dx+(y+1)e-xdy=0xy3dx+(y+1)e-xdy=0(y+1)e-xdy=-xy3dxDividing equation on both sides by…