A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to ƒ on [a, b]. If so, find all values c in [a, b] guaranteed by the Mean Value Theorem Note, if the Mean Value Theorem does not apply, enter DNE for the c value. C = D = f(x) 5 ln(x) 2 ― on [1,20] (Separate multiple answers by commas.)

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Q: Problem #6: Consider the same system as given in the previous problem: 4x² + 5y4 = 9 (2xy(1²-12²) =…

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A: we use the method of substitution to evaluate the given integral.

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A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

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A: We have given sum of seriesWe have to find simple expression for the series

Q: SOLUTION If f(x)=5x2 - 1 40 In(x), then 1 f'(x)= 10x 40x 1 + [f 1 + [f'(x)]² p>'(x)]² = - ( 1 10x…

A: S(x) = 5x2 + (1/40) ln(x) - 5

Q: Evaluate S 6x In (5x)dx. 1/5 S 6x In (5x)dx= 1/5 (Type an exact answer.

A: The given integral

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A: Given:a function To find:critical points, monotone intervals and extreme points of function f(x).

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A: (a) Compare the  and  to get

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A: Given:  To Find: To determine the equation of .The range of .The x-intercept (if any) of .The…

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Q: #3: Find the maximum of f(x, y) = 19 ln(18x6y6) + 43 subject to x² + y² = 25, x > 0, y > 0.

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A: The given vectors .The objective is to find the vector that is perpendicular to both  and .

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A: The answers are given below please have a look.Explanation:

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Q: #6: Consider the same system as given in the previous problem: 5xu² + 4y14 = 9 3xy(²-²) = 0 It is…

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Q: Consider the right triangle shown below where a = 10.34, b = 10.86, and c = 15. Note that and are…

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Q: 5) Find the general solution of the non-homogenous differential equation: dy = dx x + y +4 4x+4y+8

A: Explanation is given below:(ask in comment for any doubt!! )Explanation:

Q: Consider the same system as given in the previous problem: 4xu²+5yv4 = 9 3xy(u² - v²) = 0 It is…

A: The correct answers are:(a)dxdu​=0 at(1,1).(b)dydv​=0 at(1,1).For further explanation check…

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A: Solution is done.Explanation:Approach to solving the question: Detailed explanation: Examples: Key…

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A: Cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product…

Q: If H (x) = x² (2x-41)

A: H(x)=x2(2x−11−4x)

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A: Question explained below:Explanation:ANSWER :​​

Q: If f(x)=√√x²-1 and g(x) = x+1, which expression is equal to f(g(x))? + 2x (x+1)²-1 +x-1

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A: The correct options are:1) D2) A3) CExplanation:

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A: Here given that a graph and we find the equation of the function by using  this graph.

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A: To evaluate the integral   use the following substitution.

Q: Use implicit differentiation to find ?х and ду for x6 + 2y²+ 3z4 = 1

A: