Evaluate the following Integrals: 1. 6x² sin x³ dx

Q: 2. lim f(x) and lim f(x) if f(x) = V4-x2 %3D X-2+ X→2- х-2

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Q: Bottled Water Sales The following chart shows annual per capita sales of bottled water in the United...

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Q: Consider the following differential equation. y"-y'-30y 0 Verify that the functions .-5x and 6x form...

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Q: 1. If f, g, and h are odd, integrable functions, and a is a real number then a | (1)i+ g(t)j+h(t)E) ...

A: "Since you have asked multiple question, we will solve the first question for you.If you want any sp...

Q: The demand function for a company's product is p 24e-0.99 where g is measured in thousands of units ...

A: Given: p=24e-0.9q  

Q: Integrate the rational function by partial fraction (decomposition): 2-9-dx r3-9x

A: Let I=∫x2-9x-9x3-9xdxApply the Sum Rule:  ∫fx±gxdx=∫fxdx±∫gxdxI=∫x2x3-9xdx-∫9xx3-9xdx-∫9x3-9xdxI=∫x2...

Q: Evaluate the definite integrals using the graph of f (x) below. 4- y 2- 2 10 12 -2- -6 (a) Number (b...

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Q: 04 +C 3lne d0 = 2e (A) True B False 2.

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Q: 2e*dx where e = 2.7183 %3D

A: Given: I=∫012exdx   As we know from the integral; ∫a·fxdx=a·∫fxdx, where 'a' is the constant. And ∫e...

Q: general function M(x, y) or N(x, y) so that equation is exact.

A: We will find the function (general). 

Q: A. converges B. diverges

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Q: (In(x))? 3

A: We have to apply rules of integration to solve the problem

Q: A scientist places 2222 mg of bacteria in a culture for an experiment and he finds that the mass of ...

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Q: 2メー7 f xス」

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Q: 1.Determine if the following statements are mathematical or not. Provide solution. a. Today is MMW c...

A: We know a mathematical statement is either true or false .

Q: What is the range of g(x)( 1/2)^x - 4

A: Topic:- algebra

Q: Integrate the function f (x, y) = 3xy over the region bounded by y = 32x2 and y = √x

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Q: y = C,e²x cos(3x) + C2e2x sin(3x)

A: y=c1e2xcos3x+c2e2xsin3x  differentiate with respect to x dydx=C1(e2x3(-sin3x)+2e2xcos3x)+C2(e2x3cos3...

Q: Find the Laplace Transform of the given function. Show your solution completely and box your final a...

A: Given that: f(t)=t2sin2t

Q: and horizontal lines), without performing the integration. (c) Write down the integrals with their l...

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Q: (siny – 2ye*sinx)dx +(cosy + 2e*cosx)dy = 0

A: Given differential equation (sin y -2ye-x sinx ) dx+ (cosy+2e-x cos x ) dy=0

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous fu...

Q: y'dx-(sy + y* }ky = 0 1. Let the substitution y=2; y=vx; dy=vdx + xdv

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Q: The functions f and g defined by F(x) =-2÷[|3x-9|] G(x)=x^2 + 9 -[ square root( x+4)÷8]-4 Respective...

A: Given:   To determine: The domains of both functions

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic ...

A: We will find the T2(x) and T3(x) for the given function.Below find the solution in the image.

Q: Solve the following second-order differential equation: y" + 4y' + 5y = 8x sin æ

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Q: (x) = x^2 +3x-4, which of the following represents the solution for the equation?

A: Topic:- algebra

Q: dy 9x using 5. Find the slope field of dx GeoGebra.

A: This is a problem of the slope filed plotting. In this given question dy/dx is representing slope of...

Q: Findthe volume of the solid obtained by rotating the region bounded by the given curves. y=radicalx ...

A: Given Equation y=√x ,x=4 and y=0 

Q: 3. The function (x, y)= 8r-/4x +3y is homogenous in x and y of degree 2х 4. The function (x,y)= (x' ...

A: Here ,                We have given some of functions f(x,y) which are homogeneous in x,y so we have...

Q: 24 Let 6n an 7 – 4n For the following answer blanks, decide whether the given sequence or series is ...

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Q: Agree. then lim f(x) does not exist. Disagree 3. If f(a) is undefined, Justify:

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Q: x*dy + (2.xy – y² }tx = 0 Let the substitution y=2; y=vx; dy=vdx+ xdv

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Q: A company's total cost, in millions of dollars, is given by C(1) = 130 -60e where t is the time in y...

A: The company's total cost, C(t)=130-60e-t

Q: Which of the following is not true? (A) - |f(x) dx- J8 (x) dx B) 8 (x) dx C) (x)dx=k (D) O fas(3))dx...

A: some properties of the integration are given, we have to find the not true statement.

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: topic - application of derivatives

Q: Find the limit, if it exists: (Do not use L'Hospital's rule) (V42 lim 4x2 4а* + 16х V + 20 Note: Giv...

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Q: 1. Determine the area under the curve y = x² + 5 from xX1 = 0 to x2 = 1.

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Q: Which of the following answer choices give the equation of an asymptote for the graph of f(x) = tan ...

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Q: (a) y = -T (b) y = 2x° + 3x (c) y = x² + 5x 7 (d) y = x(x - 1) %3D -

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Q: Suppose a product's revenue functio is units sold. Find a numeric value for the margin The Marginal ...

A: Marginal Revenue(M.R) is defined as the derivative of revenue function               M.R = d/dq[R(q)...

Q: Suppose the cost of producing bananas is given by the differntial equation: dC/dx = 26/x + 45x whe...

A: The cost of producing bananas,dCdx=26x+45x

Q: f(x)=10/17sqrt(6x2+2x+6) =10(6x2+2x+6)

A: The given expression is: f(x)=10176x2+2x+6=106x2+2x+6

Q: Find the set of points satisfying the equation in the complex variable z: |z* + 2i| = |F(z – 3i)| wh...

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Q: Recall from our lesson that a Non - Homogenous 2nd Order Differential Equation has 2 sides: The Char...

A: Given that, There are two differential equations following, (i). y'' - 3y' - 10y = 5e-2x (ii). y'' +...

Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: Suppose that for each i such that 1 <i<N one has / f(1)dt = i Ji-1 What is / f(t)dt if N = 87?

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Q: II. Application of Derivatives 3. Find the tangent line to f (r) = (2– 4x²)° at z = 1.

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Q: të the area covered by the curv om xi X2

A: Given query is to find the area bounded by the curve from x= -1 to x = 1.

Q: 4. (3 coshm +ecoshm sinhndm

A: Given that: ∫(3ecoshm+ecoshm)2.sinhm.dm