(a) x²ex

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A:

Q: 4- Use the series to evaluate lim x-0 ex-(1+x) x²

A: By using the series to evaluate the following limit.

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A: Volume of solid obtained by revolving the region about x axis is given as followsGiven functions

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Q: +³ 3 y=a+t, √a ≤ t ≤ √a X || +at,

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Q: Evaluate the following integral. 16 1 dx 8-√√x

A: The given integral is

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A: The equation of the curve is

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Q: find Maclaurin Use of f(x) = Then write terms, generalize Write the e ratio 5x out series test…

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A: To find the total area between the region?

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Q: Solve the initial value problem below. x²y"—8xy'+20y =0, y(1)=−1, y'(1) = −8 y =

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Q: Use the method of Lagrange multipliers to solve this exercise. Hercules Films is also deciding on…

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Q: 24. Find the equation of the plane that contains the points (5, 0, 4), (1, 3, 3), and (3, 1,3).

A: Given dataPoints of a plane,

Q: (-1)"(36)" (2n)! Use a McLaurin's to find round your answer to four digits after the decimal sign.…

A: By using a MacLaurin's to find.

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A: We have to evaluate the integral.

Q: B: Find General Solutions for the following Differential Equations (Use Differential Operators) (D²…

A: we have given differential equation

Q: 1 Let f(x)=x²e² the value of — lim [ƒ(x)]¹/* i is: a) b) 1 d) 1 e c) 0 1 -19 4e

A: Given that a function f(x) and we find the value of limit.

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A: The given matrix

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A: We have to write down a diffrential equation of the form  whose solutions all approach  as

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A: The given differential equation

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Q: If r=ctheta, how do we simplify this integral. If anything, what is dr/dtheta? r + dr () 2 de

A: The given polar equation  The integral need to simiplify

Q: Q3/ A: Find General Solutions for the following Differential Differential Operators). (D² - 4D + 4)y…

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Q: Find and simplify each of the following for f(x) = 8x-9. (A) f(x + h) (B) f(x+h)-f(x) f(x+h)-f(x)…

A: f(x)=8x-9

Q: Simplify the expression if ||v|| = 10 and ||w|| = 9. (Give your answer as a whole or exact number.)…

A: (i) commutative law ,    A.B=B.A(ii) Distribution law,  A.(B+D)=A.B+A.Dlet  K=(v+w).v-(v-w).w

Q: Find the indefinite integral for the function using the substitution u 4x² + 5. ] [ V432+5 dx

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Q: A small cannonball with mass 9 kilograms is shot vertically upward with an initial velocity of 180…

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Q: Below is the graph of f(x). Determine the following. (a) f(-2) = b) f(-1) = h) f(2)= 1) f(3) = " 3 2…

A: We are authorized to answer three sub parts at a time, so we  are answering the first three…

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A: given position vector is

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Q: 11² F = (eª sin y, eª cos y, yz²) S is the surface of the box bounded by the planes x = 1, y = 2, z…

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Q: Determine and state whether the following series converge or diverge. Justify the answer

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Q: ро b) Point P (3, 7) is in coordinate. Express this point in cartésion coordinate

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Q: a) Solve for a if Σ(3a)" = 4. 1 m=1

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Q: 4. If you are given $30 every year on your birthday, and put it straight into a bank account that…

A: Principal amount Interset rate According to Recursion formula:    where