Determine the center of mass for the region bounded by the following y=x^3 and y=√x.

Q: Evaluate f 2x dx 2-1 Solution Steps Rewrite rational expression to exponential expression to make…

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Q: ydy J-7-By-y

A: Given problem:- ∫ ydy/√(-7-8y-y2)

Q: 8. The general solution of y" + 4y = 3 sin 2x

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Q: -6(х— sin "x)(csCx «)(cs 3 CSC X |

A: Topic:- function and trigonometry

Q: х3-4х-10 х2-х-6 (2x + 21n|x – 31 – 4 In |x + 2|) + C (2x + 2 In|x – 3| + 4 In |x + 21) + C Option 1…

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Q: 5. (a) Let z = (a+ ai)(b+ bv3i) where a and b are positive real numbers. Without using a calculator,…

A: See the answer below

Q: Find the first derivative of y = cos4 x – sin4 x and y = x3   –  x2 cos x  +  2x sin x  + 2 cos x…

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Q: ( 19 ' Evaluating cot 3 will yield to A 3 B -V3 D

A: Here, cot19π3cot6π+π3

Q: Find the first derivative of y = ( ex – e –x ) / (ex + e –x ) and y = ln [ x + √ (x2 + 1) ]…

A: y = ex-e-xex+e-x,Differentiate w.r.t.'x'Apply the Quotient…

Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0 %3D

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Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: x + 2 x + 1

A: ∫x2+2x+1dxSubstitute u=x+1→dudx=1→dxu=dxx2=(u-1)2 =∫(u-1)2+2udu=∫u+3u-2du

Q: (Wh(2 - h)dh

A: To evaluate: ∫(h(2−h)dh Let I= ∫2h12−h32dh

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: 10. Simplify as much as possible: log (

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Q: D. Define the multiplication operation * as modulo 10 in G = {1, 3, 5, 7,}. Cr table for this.…

A: Topic:- algebra

Q: What is the slope of the tangent line to the curve a +y +¢y=3 at the point (1, 1)? O -1 O 1 cannot…

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Q: Calculate the following limit: lim( lim(3) e-5z+6 2-9 O 1/6 0 1 O does not exist

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Q: (3x-2) dx x²+ 2x + 15

A: the given problem is solved below in detail.

Q: TT Sz sin? Bcos? Bdß 2

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Q: Two particles have positions at time t given by S1= 4t - t2 and s2 = 5t2 - t3. At the instant the…

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Q: . Evaluate the following: (ey)dy dx A. e -1 2. В e-1 С. 2е +7 D.

A: Given query is to fins the value of the integral.

Q: If a rocket travels according to the function s = 5t3 after takeoff (where s is in %3D meters), then…

A: Velocity is obtained by differentiating S

Q: A box with no top that is twice as long as it is wide has a volume of 36 m3. If x is the width of…

A: A box with no top that is twice as long as it is wide has a volume of 36 m3.

Q: a. You are about to eat a slice of pizza and decide to do a little PreCalculus first. The entire…

A: Let's find volume of slice of pizza.

Q: - The demand for your item is given by the following function 2 - 8z (z-8)(z² + 3) Find what number…

A: The given demand function Dx=-x2-8xx-8x2+3+100, so, x≥0. To find the number of products to be sold…

Q: Area under the curve xy = -1 from x=1 to x=2

A: topic - area under the curve

Q: 3. 2x°- 2x) dx x²+10 2 t1o

A:

Q: Find the 23rd derivative of y = -sinx Select one:

A: We have to find 23rd derivatives of y=-sinx

Q: (D- 3)'( D + 9)y = 0

A: We can solve the give ODE as follows:

Q: Compute for the indicated power of the following: (-võ + iv2)*

A: Please refer to the image below

Q: 19. For the following function f (x) 3x-4 %3D find any x-intercepts, y-intercepts, and equations of…

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Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: Supply the missing integrand and the limits of integration sinx dy dx _dx |1– y²

A: Solution is given below:

Q: ди and az ди ди Find дх ду (whenever possible) for the following functions. 1) u = 3x²y + xlny² –…

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Q: 6. What can you conclude when dy is changing dx from positive to negative? A) fis at a local minimum…

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Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

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Q: 3. Find the reference angle (also called the reference number) for the angle: 13n radians. 11

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Q: 8. The price-supply and price-demand equations of a certain product are given by p = S(x) = 15 +…

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Q: (a) Find the equation of the tangent line at A. (b) Find the area of the shaded region enclosed by…

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Q: 10. In writing a function in the denominator and its derivative is in the numerator, which of the…

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Q: cx+ln x Determine the equation of the tangent line to the graph of f(x) cosh (V2t – 1) dt at x = 1.

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Q: Direction: Translate the following notations into statements in terms of the area under the curve.…

A: LetI=∫212dxWe know that ∫abfxdx=-∫bafxdx, a<bThereforeI=-∫122dxTake constant outI=-2∫12dxWe know…

Q: A ladder of length 15 meters is leaning against the side of a building. The foot of the ladder is…

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Q: General solution of x dy = (2xex – y + 6x2) dx %3D

A: The given equation is: x dy=(2xex-y+6x2)dx That can be written as:…

Q: Consider the following limit. Find the limit L. L = (a) Find & > 0 such that |f(x) - L 0 such that…

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Q: 17. If you knowf (0) = 625 and f(4) = 16 then: (a) Find a formula for f(x) assuming that it is…

A: In this question, we want to find a linear function f(x) which satisfy the given conditions.

Q: -3 2. Evaluate: V12-피 + z dar 0,

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Q: Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial…

A: Given:       y=arctan3sinx4+5cosx First derivative:     dydx=ddxarctan3sinx4+5cosx…

Q: 1) Find the radius of convergence and interval of convergence of the series. Show All Your Work.…

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