Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval, and indicate the x-values at which they occur. f(x) = x° - x² - x + 3; [0, 2) 8- 6. 4-

Q: 1. Given z, = 5 cos 377 +i sin 37 and z2= 37 +i sin 2 find z,z2 where 0se< 2x. cos 2 2 37 +i sin 2…

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Q: Bones from the skeleton of a fish have lost 30 percent of their carbon-14. Note that for carbon-14,…

A: Formula  Given  k = 0.000124 It lost 30 percent of carbon  The left is 70 percent

Q: 3. The value of a certain baseballcard (in dollars) tyears after 2015 varies according to the…

A: Given function describes value of card t years after 2015

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A: Here, the required plane is perpendicular to the vector n=-2i+8k.

Q: Find a and b such that v-au bw, nhere u-(1, 2) and w- (1. -1) v - (4, 5)

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Q: Find the arc length of the parametric curve. x = e', y= et, V2t; 0<t<8 z = L =

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Q: Find the vector component of v = (4, – 1, 7) along b = (4, 4, -7) and the vector component of v…

A: Given,            V= &lt;4,-1,7&gt;            b =&lt; 4,4,-7 &gt;

Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: The domain of the function is the set of all possible input values for which function is defined .

Q: 4. For each of the following, state whether the equation is ordinary or partial, linear or…

A: here derivative of first order so order 1 here power of x is 2 so non-linear and ordinary equation…

Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

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Q: 2x) dx Find an approximation to the integral using a Riemann sum with right endpoints and n = 8.

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Q: 13 For the sequence an = n +1' its first term is its second term is its third term is its fourth…

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Q: Question 5 Find the volume of the solid that results when the shaded region is revolved about the…

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Q: S) Vx + 7 dx

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Q: Eliminate* the arbitrary constants c1 and c2 from the relation y = cje-2* + cze³* у" -у — бу %3D 0 O…

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Q: e2x :dx /1– ex

A: Given:        ∫e2x1-exdx  substitute u=1-ex→dudx=-ex→dx=-exdu  use e2x=1-u2      =∫u-1udu Expand:…

Q: (b) Determine the by using the Chain rule with the following information: z = cos (x"y^) – sin (z +…

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Q: ii, Calculate the volume and surface area of a solid cylinder 1.5 m diameter and 2.5 m tall.

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Q: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: The sum of the geometric series 1 3-1+ 3 1 + 9. 1 +- 81 - 27 is: none 13 914 OO O

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: f (x) = (x³ – 5x + 2)(x² + x – 7); find f'(x) %3D

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Q: A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both…

A: Given and Basic information:R=Rn, Revenue earned by selling 'n' tiresdollarsC=Cn, total cost of…

Q: Find the mass and center of mass of the lamina bounded by the graphs of the given equations with a…

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Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: dz (a) Find of the following functions: dx 2+1 +cos y? = sin(y'+ 22z) COS 7 ZX %3D

A: Solving

Q: Find the divergence of the vector field F = < ya®, æ2®, zy* div F = Preview

A: Divergence of F→=yx3, xz6, zy4

Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy? *…

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

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Q: Find cos 0, where 0 is the angle shown. Give an exact value, not a decimal approximation. cos e = 17

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Q: c) Determine a pattern for the value of the even, (2k)", derivative of f(x) at x 37T th d) Determine…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Solve the equation: xydx + (x² + y²)dy = 0 O y²(2x² + y²) = c O 2y(2r² + y²) = c

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Q: dx 7. S; x³ Vx2-4

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Q: Describe the graph of the equation. r = (8 - 3t) i - 14t j O It is a line in 2-space that goes…

A: Let's find.

Q: Question 3 Assume y is a differentiable function of x which satisfies the following equation: y2 +…

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Q: Consider the following. u = 3i - j - k, v = -i + 5j + 7k (a) Find the projection of u onto v. (b)…

A: A detailed solution is given below

Q: Determine whether the following series converges or diverges. Σ 5n2 +5 n=1

A: We can solve the given problem as follows:

Q: Evaluate the definite integral. e4t i+ e-j+t k)dt O et – 1 – (e-1 – 1). 4 2 O e4 i – 1 j + k 4 (e* –…

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Q: Lets compute a derivative in reverse! Given the function f(r) = e² + sinhr + + z find a function…

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Q: x2-25 The limit of the function f(x) = as x approaches 5 is equal to -10. 5-x TRUE FALSE

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Q: Find the centroid of the area under the curve y = x² from x-2 to x-4.

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Q: Consider the function f(x) = 3x – 2x on the interval [- 3, 3]. Find the average or mean slope of the…

A: We know that the average or mean slope of the function f(x) on the interval a, b = f(b)-f(a)b-a

Q: The limit of a constant is always a constant. O FALSE TRUE

A: To proof the limit of a constant is always a constant. Let the function fx=k, here k is a constant

Q: x2 – 25 dx 7) S-

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Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: Determine if the series converges or diverges without using the different tests discussed in Lesson…

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Q: Solve the following differential equation using variation of parameter. 4y" – y = xe"/2; y(0) = 1,…

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Q: For each of the following series determine if the series converg for series convergence or…

A: Given

Q: of the curve defined by x=3t-t anc

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Q: The function given below is discontinuous at x = 1 - 4 I1 O TRUE O FALSE

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