Sketch the region enclosed by y = eº y = e⁹, and x = 1. Decide whether to integrate with respect 5x " to x or y. Then find the area of the region.

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A: Please refer to the image below

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Q: an = Inn √n

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A: The given complex number is -3i

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A: Explanation of the answer is as follows

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A: If function f(x) is a quadratic equation, Then f(x) changes direction once.

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A: Given data÷ fx=3x+1071-x6 Find the first derivative f'x. Useful formula ddxxn=nxn-1…

Q: Find the derivative. F'(x) if F(x) = (ex5+1) 8 ='(x)= ***

A: We have to find derivative

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Q: Problem 6 convergent. The series is Justification: Determine whether the series n=110 is…

A: See this solution in below

Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

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Q: 27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ - 3x (3x + 4 if x ≤ 0 if 0 < x≤ 1 1<x<2 if…

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Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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A: Given, f(x)=2x2-4x+5

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Q: t: It F is conservative, the integration may be F(x, y) = yi - xj (a) r₂(t) = ti + tj, ost≤1 (b)…

A: Follow the procedure given below.

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A: We have to find percentage rate of change

Q: (2x - y)dx(x + 4y)dy = 0

A: As per the rules, we can answer only the first question and other can be reposted.

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A: Polar coordinates

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Q: Find y' and the slope of the tangent line to the graph of (3x-2y)5 = 2y2-9 at the point (1,2). y'=0…

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Q: f(x) =l10x2 -4xI , g(x) = 9x - 6;Find (f ∘ g)(1).

A: This question can be solved using the concept of composition of function.

Q: b) Find the derivative f'(x) in the following cases. 5x+1 1. f(x) = 2x-1. 2. f(x) = 3. f(x) = csc x…

A: We will find the derivative of given function as shown below

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Q: (D+2x)(D-3x)

A: Follow the procedure given below.

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Q: Solve the initial-value problem 1. (D² + 4) v = 12; y(0) = 0 (0) = 2

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Q: In the last part of step 1 for ds/dx, where does the 1 under the square root go? Why does it just…

A: Let's solve.