For f(x)=(x^2+x−2)/(x+2) does the Mean Value Theorem apply on the interval [0, 2] and why?

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A: solve integration  2sinA.cosA=sin2A 2sinAsinB=cos(A-B)-cos(A+B)

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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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: Given: f(x)=e3x, c=0

Q: Question 1: Differentiate the functions. a) f(x) = 2 – 5cosx +x4 + 3* b) f(«) = +

A: I am attaching image so that you understand each and every step.

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

A: By using the definition of Taylor series to find the Taylor series centered at c for the given funct...

Q: Í sinh(1 - 4x) dx Answer:

A: In this question we have to find the Integration.

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Q: Use polar coordinates to calculate the volume of a sphere of radius R.

A: This question is based on application of polar coordinates integration.

Q: (4t°y – 15t2 – y) dt + (tª + 3y² – t) dy = 0.

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Q: 5. Use the integral test to determine the values of p for which the series below will converge. 1 k(...

A: Here we have to use the integral test to determine the value of p for which the series below will co...

Q: Y and 2 Y if x dx? 七 and yo

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Q: Calculate the differential of the following function. Z = 2x³ex? + In(x+y²)

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Q: 7. 4. A firm's marginal cost and revenue functions are given by MC- 12e + 16a + 20 MR = 100 -29 a. R...

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Q: Find the derivative of y with respect to t.   y=t(ln2t)^(2)

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Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan (3x)[6x...

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 + 6x(t...

Q: Q3) A) Graph the two equations and find the points in which graphs intersect x+y = 0, y= -(x- 1) TA ...

A: A) The graph is shown below:

Q: In a study during the 1970's, it was found that one model of legislative turnover in the country A p...

A: We have to find the continuously serving members.

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Q: 8. A parallelogram ABCD has vertices A(1, –2,6), B(3, –3, 12), and C(6, –2, 1). a) Determine the coo...

A: The diagonals of a parallelogram will bisect each other. So the mid point of the two diagonals will ...

Q: Tutorial Exercise Find the indefinite integral using integration by parts with the given choices of ...

A: As we know that; The Power law; ddxxn=nxn-1 And ∫sinax+bdx=-1acosax+b+C∫cosax+bdx=1asinax+b+C Where,...

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

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Q: dy/dx = 8y-1 a, Solve with separation of variables method b, Solve by integrating factor method c...

A: topic -  differential equation

Q: Using appropriate substitution, the integral S e t3 dx is equal to:

A: ∫ex-3dx/x4 now substitute u = x-3 du/dx = -3/x4 dx = -x4du/3 ∫ -eudu/3 (-eu)/3 + c now put value of ...

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Q: 6 (a). Let f be a differentiable function with f(0) = 1, f'(0) = 2. f(x) + f(2x) + f(3x) - 3 Find li...

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Q: Q.2\Prove the Maclaurin series: (-1)"-1xn In(1+ x) = En=1' ,-1<x<1.

A: We have to prove maclaurin series.

Q: An+1 to determine if the sequence { ne" } is strictly increasing or strictly decreasing. an Use the ...

A: By see this solution in below

Q: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt. W...

A: assume that an airplane is flying toward you at a constant height, h miles, and at a speed dx/dt. Wh...

Q: . Given the point Q(1,-2,4) and a plane p: 3x + 2y + 6z = 5, find a) The distance from Q to p. b) Th...

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Q: (x5 + y5) dx + (5xy4–2y+1) dx = 0 (a) Show that the given differential equation is exact. (b) Solve ...

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Q: Solve the given differential equation by separation of variables. xy + 7x - y - 7 xy - 2x + 8y - 16 ...

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Q: 03) Evaluate the following integrals: A) y = sec(tan-1x). tan³(tan-1x) 1+x2 dx

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Q: 8. . cos?rsin®x dx. COS 프2

A: Product Rule of integration : ∫u.v dx = u∫vdx -∫(dudx∫v.dx)dx dsin(x)dx=cos(x)  and dcos(x)dx=-sin(x...

Q: Assume y(x) eaa cosBx is one of the solutions of the DE y(3) – 3y" + 7y' – 5y = 0. - Then α β (A) 3 ...

A: The given question can be solved as shown in step2.

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x2 – 6xy + y3 = 24

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Q: 2r (1- lim

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Q: Evaluate: dx using 8 intervals the trapezoidal rule

A: Using trapezoidal rule to evaluate the integral.

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Q: The Differentiation to be made must be based on the following topics. - Power Rule Give 3 examples w...

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Q: Evaluate

A: We will evaluate the integral. 

Q: Order the functions from slowest growing to fastest growing as x -o: 4x², (In x)³, 10*, and e2x

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Q: Given f''(x)=7x+6 and f'(−1)=−1 and f(−1)=1.   Find f'(x)=    and find f(3)=

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. 5+ 27 1....

A: topic  -series convergence and divergence 

Q: Integrate S (a?- ) dv ; where " a" is constant O = - + C 3 =-{ (a? – v²)* + (a? – v²)* + C O = (2? –...

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Q: Par (+a) 1.

A: Solving the problem by doing the substitution.   NOTE :: As per our Expert guidelines we are suppose...

Q: In a certain electronic factory, the ratio of the number of male to female worker is 2:3. If one hun...

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