Use series to evaluate lim 4x2 (e -2/x -1). ... lim 4x (e -2/x -1) =D X00 (Simplify your answer.)

Q: dP 5. = P- p2 cet Ans: %3D %3D dt 1-P

A: topic - differential  equation

Q: 1. y = x° + x

A: answer is in next step

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A: The given differential equation,dydx=e3x+2y

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A: A detailed solution is given in step 2.

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Q: 1.) Í 9r*dr/V1- r 2.) csc c²20cot20d0

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A: To find the value of x, y.

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Q: x+x+1 Use partial fractions. 2x2+2+x3+x

A: The given integral is;  (x2+x+1)/(2x2+2+x3+x).

Q: Write the complex number in standard form. (2-J-15)* O -11+ /15i O 4- 15/5i O-11-4/15i O -11+4/15i…

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Q: Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x)=…

A: Given functionf(x)=xx-4

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Q: (In x) ² dx,u Use integration by parts.

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Q: | (In x)? dx. 1. Use integration by parts.

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Q: (0) (4) | 童 9. 4. 2. 2. Question 4 OE OB () 91 3. (a) (V) (B) What is the area of the region between…

A: Given query is to find the area bounded by the graphs.

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A: We have to write the given first order differential equation in standard form .

Q: Decide which of the following regions has n () in area = lim tan 2n 2n i=1 without evaluating the…

A: To decide which of the regions has the given area.

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Q: ||r(t) × r"(t)|| ||r()* Use the formula k(t) to find k(t). r(t) = 8 cos(6t)i+8 sin(6t)j+ 7tk K(t) :

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Q: On a hot summer afternoon, a city's electricity consumption is  −3t2 + 12t + 10  units per hour,…

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Q: Find the derivative of the function. f(x) = In(sinh(x)) f '(x) =

A: f(x) = ln(sinh(x)) here we use chain rule f'(x) = cosh(x)/sinh(x) f'(x) = cot(h(x))

Q: Find the following Laplace and Inverse Laplace Transform of the function. 5. f(t) = e-4t (t-cos(t))

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Q: Calculate the vector line integral F. dr. where Fis the vector field (z+ Sy, 2z - y) and Cis the…

A: To find the value of the given line integral.

Q: A (x -3) dy X +y -.

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Q: Given the differential equation 5 y" = 7xy' Use Reduction of Order and the letter "R" to reduce the…

A: Let y' = R So, y'' = R'

Q: Find the indefinite integral. (Use C for the constant of integration.) 1 dx xV 16x2 – 1

A: Solve the  intregal

Q: Convert the polar coordinates (0,23°) to Cartesian coordinates. (0, 0) (23, 0) (0, 23)

A: Explanation of the answer is as follows

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Q: v du is? x³ sin (x²) dx ¡s evaluated using IBP, the value of J When

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Q: 17 i

A: Explanation of the answer is as follows

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Q: 10 | Vx3 + 6 dx, n = 4

A: Given

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Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: Find the largest number d such that if |x - 2| < 8, then |4x – 8| < ɛ, where ɛ = 0.5. Repeat and…

A: Solving

Q: In circle B with mLADC=43 find the measure of minor arc AC. B C. A The measure of arc AC =| %3D

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Q: Given f''(x) 25 sin(5x) and f'(0) = - 1 and f(0) = 2. | Find f() 6.

A: Given query is to solve the differential equation and find the valu of indicated function.

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Q: 8. xy +y2 - x²y' = 0

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Q: Find the area bounded by the lines and curves y = x? - 2 and y = 2

A: Graph:

Q: 27. Jul 16,0 =

A: Given data÷ Vector u is given by u=ucosθi+usinθj Or  u=&lt;ucosθ,usinθ&gt;

Q: Express the polar coordinates (V2, -) as Cartesian coordinates. O (-2, -2) O (-1, -1)

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Q: Fnd the gradent vector feld o S(2,9) = VEz+ y. Provide your answer below

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Q: ² V1-x² dx x2 Use trigonometric substitution

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Q: For the integral, / tan'x sec*x dx, if we let 4=tan x, what is the re-written form of the integral?

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