(a). Determine whether the Mean Value Theorem applies to f(r) = x In x on [1, e]. (b). If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.

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A: This question is based on application of integration.

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A: Please refer to the image below

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A: This question is based on factorisation of trinomial and percentage.

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A: Given:     Limit is given

Q: End the solution and dyined the interpal at which function is depince dx

A: Given that xdydx+y=1y2Solution :xdydx+y=1y2xdydx=1y2-yxdydx=1-y3y2y21-y3dy=dxx∫y21-y3dy=∫dxxlet, 1-y...

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Q: (a) State if the following are True or False. You need not show any working. (i) f(t) = (t³)(t°) is ...

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Q: Which of the following is an identity? sinBsecBcotB = sin²B/cos²B sinBsecBcotB = 1 sinBsecBcotB = c...

A: sinBsecBcotB  secB = 1/cosB  cotB = cosB/sinB  So now put all this value in given function  sinB(1/c...

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Q: State the characteristics. -2 esc 7(x- 190° ) + 5 こ a inc. period = H.S. = Y.S=

A: Find your answer below 

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the seque...

A: In this question we have to find whether the given sequence is converges or diverges.

Q: 2 ne-n?

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Q: _3. The equation of the tangent line to the function f(x)=-- at (-5,) is x-3 7. y = x- 25 1 25 4. Th...

A: Topic:- function and derivatives   

Q: Evaluate the following limits. + Vw)(2 – w² + 3w*) 1. lim (1

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

Q: Find the area of the region enclosed by y = 4.75x and z = 9-y". -2 1 2 3 4 5 6 7 8 9 -1 Use horizont...

A: here y =4.75x x=9-y2 we have to find y so y/4.75 = 9-y2 y = 42.75 - 4.75y2 4.75y2 + y -42.75 = 0 y=2...

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Q: The function g is defined by the following rule. g («) = G Find g (x) for each x-value in the table....

A: solution:-g(x)=17xg(-2)=17-2=72=49g-1=17-1=71=7g0=170=1g1=171=17g2=172=149hint,a0=1a-1=1aa is consta...

Q: Use the ALEKS calculator to evaluate each expression. Round your answers to the nearest thousandth. ...

A: topic - logarithmic functions 

Q: Set up the integral to find the length of the curve f(x) = V1 – 2? for 1/v2 <x < 1.

A: Please see the answer below.

Q: Find the limits of the functions below a) limx-3 x* sin x b) lim,

A: We can find the limit of both the question as below.

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Q: geles B=} AtC= | AtC-2D= -2 う -2D = -3 2の I +3

A: As per guidelines we can elaborate and solve your query as answer below.

Q: solve the differential equations by using integrating factor y'= (y/x) + 2x+1.       when ; y(1)= 3

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Q: In 2010, 1250 U.S. college students expecting to graduate in the next several years were surveyed. R...

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Q: (f) p(xj,...X) =E

A: Degree is n. 

Q: a) State if the following are True or False. You need not show any working. (i) z = 2 – 2i has magni...

A: To state whether the given statement is true or false.

Q: Your equation to represent the amount of money that Dahlia earns for babysitting as a function of ti...

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Q: - 3x 2 + (コメオリ)』 = e Jス

A: Given: - The differential equation is, xdydx+(3x+1)y=e-3x To solve: - The solution of the given equa...

Q: Essential Question How do you evaluate cube roots and square roots?

A: Asking: show all thr details step by step to finding cube root and square root. 

Q: Determine the function f satisfying the given conditions. f'(x) = -3x2 8. -3 f (3)= 8. f (x) = %3D

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Q: A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed...

A: Cooling

Q: Consider the following functions. f(-3) = 14 and g(-3) = -11 Step 4 of 4: Find |(-3). Answer How to ...

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Q: sin³ydy |1+ cosy The is equal to 1 A.cosy +, cos²y+C 1 B. –cosy +, cos²y + C 1 C.-cosy -, cos²y + C ...

A: ∫ sin3(y)dy/(1+cos(y)) here put the value sin2(y) = 1-cos2(y)           = (1+cosy)(1-cosy) put this ...

Q: = 4 cot -1 3. y = cos x 4. y = c Csc 2x

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Q: (4.)Consider the function f continuous on [-1,1], such that f(0) = 0, and f'(z) = { 3x2 for -1 < x <...

A: Explanation of the answer is as follows

Q: Use sigma notation to write the Taylor series about x = 8 for the function. 1 x + 5 k = OW

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Q: A rock with a mass of 15 kilograms is put aboard an airplane in New York City and flown to Boston. H...

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Q: 9. An amount of $12,000 is deposited in a bank that pays interest at a rate of 3.5%, compounded cont...

A: Given query is to find the the amount after 4 years and the interest earned.

Q: Suppose Ryan borrows $9000 at an interest rate of 3% compounded each year. Assume that no payments a...

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Q: Find all critical points of the following function. 4 f(x,y) = - 8xy + 2x* +2y*

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