Fully condense the following logarithmic expression into a single logarithm. 4 ln (2) + 3 In (3) - 4 In (4) = ln(| Number (Enter your answer as a fraction or whole number (no decmals))

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = 27 - x, y…

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Q: Solve: (1+x2)dy+ydx=0; y(1)=1, implicit solution Also: a) Determine the value of y if x=e (euler…

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Q: (D² − 4)y : 4)y = 8e²x - 12 Your answer

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A: Elimination method : In the elimination method, by using fundamental arithmetic procedures, we can…

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A: D3+D2y=0

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A: integration

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A: Given; d2ydx2+3dydx-10y=3x2 So, we can also write as; D2+3D-10y=3x2 So, the auxiliary equation is:…

Q: Which of the following is the derivative of (x³ + 1)(x² + 2x)? 3x²(x² + 2x) + (x³ + 1)(2x + 2) 3x²…

A: This question is based on product rule of differentiation.

Q: Question 15 The cost, in dollars, to produce a designer dog leashes is C(z) - 8x +9, and the…

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Q: find the total differential dz. xety

A: dz=∂z∂xdx+∂z∂ydy ---->1Consider z=xex+ythen∂z∂x=ex+y+xex+y∂z∂y=xex+y

Q: - · Find y(0-3) for y` =X²+y², y(0)=1 h=0₁1

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Q: Find the area between the loops of the limacon r = Area = 5(1 + 2 cos 0).

A: We have to find the area between the loops.

Q: 01) Solve the differential equation with the given initial condition: y' - 6x²y + 4xy = y. where…

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A: The given integral is x2/3 +8 limit from 1 to 2.

Q: f(x) = 2x + 3 x 1 1 ; a = 1

A: limx→1+f(x)=limx→1+x2+2                =12+2=3limx→1+f(x)=3

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A: Value of x for which series is convergent is given.

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Q: Find the value(s) of c such that n=0 enc = 10

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Q: Find the equations of the lines tangent and normal to the curve guen by para- metric equations at +…

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Q: Evaluate the line integral. [(x - y) ds C: x² + y² = 16 Lox (x - y) ds = C i

A: Evualate the line integral

Q: Use calculus to find the exact absolute maximum and minimum values of f(x) = (x² + 2x - 3)² on…

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Q: Find the integral of the following equation integrate (cos x)/(1 - cos^2 x) dx

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Q: Question 7 Given the function f(x) = 8 +5x², calculate the following values: f(a)= f(a+h)- =…

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Q: Write the given (total) area as an integral. • The area above the x − axis and below y = 4 − x²

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Q: the

A: We will solve the Differential equation.

Q: X (b) lim 0 DO (c) lim xln 1

A: (b). Given: limx→0+lnxx

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A: As per Bartleby guideline,  we have answered only the first question. Please repost mentioning the…

Q: = fºx R/2 Given that evaluate - b² = g², use this result and the fact that 2 (6 cos(x) - 6x) dx. x…

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Q: y" + 6y' +5y=10sin (2x)

A: First find AE(Auxiliary equation) and PI ( Particular integral)  then CS ( Complete Solution) is PI…

Q: Find the derivative for each function. ㄷ 7. y=x² +2 9. y=2x²-x+3 A. 6. y=3x²-6 8. y=x²-3x+2 10.…

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Q: The base of a certain solid is the area bounded above by the graph of y = f(x) = 4 and below by the…

A: Here, the given region is bounded above by the curve y=g(x)=4 and bounded below by the curve…

Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

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Q: IF F. dr. F(x, y) = 9xi + 6yj C: r(t) = ti + √4-t²j, -2 ≤ t ≤ 2 Evaluate

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Q: Solve for the solution: d3y/dx3 - d2y/dx2 -dy/dx +y = 0

A: Solution is given below:

Q: 2 Find az/ax if the equation yz - Inz = x + y

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Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Given problem:- A manufacturer has determined that the total cost C of operating a factory is   C =…

Q: 1. Use calculus to find the exact absolute maximum and minimum values of f(x) = (x² + 2x - 3)2 on…

A: We have to find the solution

Q: As you will show, exponential growth functions ekx always dominate power functions x", and power…

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Q: d²y_dy + y = 0 dx d³y_d²y dx³ dx²

A: Auxillary equation ism3-m2-m+1=0m2(m-1)-(m-1)=0(m2-1)(m-1)=0(m+1)(m-1)(m-1)=0m=-1.1.1  are the roots

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Q: -2x Find the derivative of f(x) = xe O f'(x)=e-2 (e-22) ²- O f'(x)=x²e-2 (²-2) O (E) None of these O…

A: We have to find the derivative of  f(x) = xe-2x.

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A: Given

Q: Question 1 (a) (b) Find the residue of f(z) Find the residue of f (z): = = sin z at z = π. 2²-3z…

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Q: r(t) = 8 cos(t)i + 8 sin(t)j + tk; T r(). 2 = = ㅠ 2

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Q: Using the Mean Value Theorem In Exercises 13-18, determine whether the Mean Value Theorem can be…

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Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: Differentiate: arcsin arccos () = 1

A: