Find the area of the surface obtained by rotating the line y = 19x + 6 about the x - axis from the point (8, 158) to the point (17,329) No decimal entries. Find the exact value. S=

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A: According to Bartleby guidelines I can only answer the first question of the two questions given.…

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A: Explanation of the answer is as follows

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A: Thr solution is given in the next steps.

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A: We have to find the rate of change of angle.

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A: Compress from the natural length through 1-0.8= 0.2 meter spring constant 'k'=16 N/m

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Q: 100 Ln=1 a. Converge 3 b. C. d. Diverge (-3)2+1 is 23n 318 338 8 b 2 2 0 J d a *

A: The objective is to check the convergence or divergence of the series.

Q: 2 Find all local extreme values of f(x) x³ + 11x²56x + 30. = 3 The FIRST local extreme value, moving…

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Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

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Q: What integration technique can be used to integrate: A Trigonometric Substitution B Integration…

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Q: -1 2 (x² +1) dx

A: To evaluate: ∫x6-1x2+1dx Let I = ∫x6-1x2+1dx Using polynomial division we get  I = ∫x4-x2+1-2x2+1dx

Q: 3. Find the equation of the tangent lines and the normal lines to the curve y = √2x-1 at x=5

A: As per the company guidelines we are supposed to answer only first question. Kindly repost the other…

Q: Evaluate 7/2 Iva each of the following:- √2 √ tane do

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

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A: We have to solve the given D. E.

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Q: A region in the first quadrant is bounded by the curve >= 1+ sin²x, the coordinate axes and the line…

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Q: Using Simpson's method ²x² dx for n = 4 is equal to Blank 1 (use 2 decimal places with proper…

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Q: dy dt when x = 2. Let xy = 3 and Find dx dt 5.

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Q: Find in each of the following. dx sin x 1. y = 1+cosx

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Q: Exercise 0.3.23. (a) Prove that the function f(x) = vex over [0, ∞). 1 1+e™ is strictly con-

A: As per the company's guidelines, we are supposed to answer only first question. Kindly repost the…

Q: Find the area bounded by the following functions/lines/curves: f(x) = 3x3 - x2 - 10x; g(x) = -x2 +…

A: Given: f(x) = 3x3 - x2 - 10x; g(x) = -x2 + 2x Let's first find the intersection point  3x3-x2-10x =…

Q: (a) Find the parametric equations for the line segment that joins P(1, 0, 1) to Q(2, 3, 1).

A: Given, P(1,01), Q(2,3,1)

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Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

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Q: 3: Fill in the blanks in the following: 1 3. 4. If = (-12, 4, 8) the position vector of u…

A: Topic:-  vector algebra

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Q: 3. Use the given graphs to sketch the graph of f(x) + g(x). Explain your process. [A3] [C2] fox)…

A: We have to solve and draw the graph.

Q: Arrange the choices in order 1,2,3.. to prove: For any sets A, B and C x (BU C) = (A x B) U (A x C),…

A: Here we have to arrange the option.

Q: TICILNIC B. Find the general solution of the following 2nd order differential equation: y* +2y + 2y…

A: Topic:- differential equations

Q: 8. y = x ¹ Arctan 4(x4)

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Q: Question 38 What integration technique can be used to integrate: (A) Power Formula Integration By…

A: Here we have to determine the integration technique to solve the given integration. =∫5dx3+x2

Q: Find the line integral along the given path C. f(x - y)dx, where C: x=t, y = 5t+7, for 0 st≤5 C √(x…

A: Topic:- application of integration

Q: 1. Prove that (a) A\B=A\(ANB) (b) A\(B\C) = (A\B)U(ANC) (A\B)\C=A\(BUC) (c)

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Q: f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

A: Here we have to find the value of a and b such that,  f(x)=-x2+ax+b, x&lt;2-ax+7, x≥2 is continuous…

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A: