Question Define R as the region bounded by the graphs of the function f(x) = x – 1, the x-axis, x = 3, and a = 5. Write the definite integral that describes the volume of the solid created by rotating R around the r-axis. You may submit your answer in unsimplified form. Provide your answer below: V= dx units

Q: dy de + 2xy = 2xe-x².

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Q: The graph shown is f(x) = sin x. What is the integral that defines the area under this line between ...

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Q: he plane y=2 inersets the elliplic pd araboloi 3=4X +y parmbola. in a Find the slope of the tangent ...

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Q: Explain briefly why the function f(x) = e" – x³ – 8 eIntermediate Value Theorem. Use IVT to show tha...

A: We will use the Intermediate value theorem. 

Q: O : (2r-3)/ar- 12x²+ 7 – 2 im |2x*-3 + Vart- 12r²4 7|} +C V4r4– 12r2+7|}

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Q: Question 10 cot (2x) Evaluate the integral Vcot (2x)- 15 cse (2x) A) --Arcsec 4 4 cot (2x) B) Arcsec...

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Q: The graph shown below is f(x) = 2x – 1. If g(x) = f(t)d t, find g '(2) AY 8. 6+ 2t + 4 -2 4 O g'(2) ...

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Q: Find the products AB and BA to determine whether B is the multiplicative inverse of A. -32 4-1 A = B...

A: A=-32-44  ,  B=4-11-1AB=-32-44 ×4-11 -1AB=-12+2     3-2-16+4     4-4AB=[-10  1-120]

Q: Find all the second-order partial derivatives of the following function. h(x,y) = x ey + 5y + 9 dx a...

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Q: 7. What is dx (x six(x)?

A: Since you have asked multiple questions in a single request we would be answering only the first (7t...

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: 5x² tan( 3x³) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find . 5/2 A 18 5/2 18 5 18 D ...

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Q: Determine whether the given series is absolutely convergent, conditionally convergent or divergent. ...

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Q: Watch the video on partial fractions with a repeated irreducible quadratic factor e and thevideo on ...

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Q: When you perform polynomial long division on the rational expression a²+3x+3 the numerator of the re...

A: The rational expression,    x2+3x+3x+1

Q: Q1. Solve the question A. Graph the curve B. Find the x-axis intersection points (Limits of integrat...

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Q: Differentiate the functions by using product or quotient rule. a) f(x) = (1 – 3x?)• e Зx+1 b) f(x) 2...

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Q: What is f'(x) given the integral function f(x) = cos Tud u? O f(x) = -2x cos( T) %3D O f(x) = -2x co...

A: The detailed solution is given below Thank you 

Q: x²dx 1. J4 –x*

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Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel. |

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Q: dx du Sk , where u= f(x), and for some constant, k. Compute. f(2). The integral reduces to ex +1 e +...

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Q: When the numerator has a higher degree than the denominator, we have to start with long division. Af...

A: It will be covered in step 2.

Q: Consider the series >. 1 1 and 1 n312 n=1 n3 + 6n n=1 Write an inequality comparing 1 1 to for n 2 1...

A: We know, n³+6n-1≥n³ for all n≥1    

Q: Find the nth Taylor polynomial for the function, centered at c. 1. f(x) n = 4, c = 3

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Q: Question 7 Consider the integral dx . Using u-substitution, what is the appropriate u and du? -2x 2e...

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Q: Solve the following differential Equations

A: Given differential equation, x2+y2+1dx+xx-2ydy=0x2+y2+1dx+x2-2xydy=0 Formulas used, ddxxn=nxn-1ddxco...

Q: Consider the following sequence: {an} = an+1 Use the ratio an - to show that the given sequence {a, ...

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Q: I. Determine the derivative of the ff. exponential functions 1. y = 8 e -4x 2. y = 15 e 7x + 3 3. y ...

A: As per our company guidelines we can answer only three subparts question at a time, but if you need ...

Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values ...

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Q: Questão 2 Check thatF(x, y) = (ez+y – y2 – cos(y))i + (ez+y – 2yx + xsen(y))j is a conservative fiel...

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Q: II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D 5...

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Q: Question 21 sin 3x Given: dxWhat is the appropriate formula to find the integral? cos2 (3x) (4- 3 se...

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Q: Vx+11-4 (b) lim- x- 5 X-5

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Q: Is the series divergent or convergent? Show solution and explanation. +oo In n E(-1)": n2 n=2

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: Explanation of the answer is as follows

Q: Express the repeating decimal as a fraction. 0.4713 43 43 43...

A: In this question we have to express the repeating decimal as a fraction.

Q: 3x What is f'(x) given the integral function f(x) = (4u – 2) du? O f'(x) = 4x-2 %3D O f'(x) = 12x -2...

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Q: Question 2 du where u= {(x) and for some constant, k. Compute /\2). The integral reduces to e + 1 A ...

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Q: 3. Find the derivative of the following functions: a. f(x) = (x² + 1)(x³ – 2x² – 1) f(x) = b. 2 + si...

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Q: x - 5, x21 (b) A function ƒ is defined by f(x)=. 1 x<1 Show that f is differentiable at x = 1. Hence...

A: We have to show our function is differentiable or not at x=1

Q: Find the nth Maclaurin polynomial for the function. 4x - 1 f(x) : n = 4 x + 1 Pa(x) =

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Q: Sow) du. #glu)- u+1 Using u-substitution, the integral reduces to a new integral evaluate the new in...

A: Topic:- integration

Q: Using u-substitution, the integral f(x)dx Srwax u+1 reduces to a new integralg(u) du. If g(u) = , ev...

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Q: is the sequence divergent convergent? {vñ - v n +1}

A: Topic:- sequence and series

Q: / 5x? tun(3x) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find f Given: 5/2 A 18 B none ...

A: This question can be solved using the concept of substitution as used in integration.

Q: 1) exist. Show your work and carefully explain your reasoning in complete Find the limit of the foll...

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Q: Use any method to determine whether the series converges or diverges. 00 (6k)! k=0 O The series conv...

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Q: dx Given: - 06-2x. Using u-substitution and transforming the integrand, find du. A 14e2xdx B 18e-2xd...

A: Given:  ∫dx7-9e-2x To Find: By using u‐substitution and transforming the integrand, to find du.  

Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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Q: d) If the coefficients are rounded off of - 0.31x + 2.73 find the absolute and relative in y x + 0.3...

A: Find absolute and relative in y