For the following exercises, evaluate the integral. 490. 491. (I-)/ Js (-1) dx sin x dx

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Q: Find the local maximum and  minimum values and saddle points of the function f(x, y) = y3 + 3x2y -…

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Q: Consider the top half of a solid sphere of radius 5, i.e. x² + y² + z² ≤ 25 for z ≥ 0. If the…

A: To solve this problem, we need to compute the total mass  m  of the hemisphere and the  z…

Q: 2. (i) Describe with a sketch the trace of the following curve in R² (t) = (t² sin(t), t2 cos(t)),…

A: The given curve is a parametric curve in R², defined by the function (t) = (t² sin(t), t² cos(t)).…

Q: Find the absolute maximum and minimum values of the following functions on the given region R.

A: Step 1:Givenf(x,y)=x2+y2−2y+1onR={(x,y):x2+y2≤4}The function is defined on a closed region. So…

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Q: 0 The matrices are 2 A = 0 4 = (22), B = ( 10 ), C = 0 - ( 1 ) -2 0 0 2 Compute the following…

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Q: Q2. [1 mark] I measure my bike tire pressure at noon, at 1 PM and at 2 PM and the tire pressures are…

A: Let's break down the solution step by step:Understanding the problem: The problem describes an…

Q: Let S be the parabolic arch given by r(u,v) = (u+v, u-v, 4-u²) where (u, v) € [−2, 2] × [0, 1].…

A: Step 1: Step 2: Step 3: Step 4:

Q: Given that t et is a solution of the constant coefficients differential equation y" + a y" + b y - 2…

A: 1. Given Differential Equation:y′′′+ay′′+by′−2y=0Compute the…

Q: Consider the following heat equation on a rod (which includes heat loss through the lateral side and…

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Q: Evaluate the following limits: g) lim(√n² +1-n) 11-00

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A: Step 1:   Step 2: Step 3: Step 4:

Q: Find parameterizations for the following objects. (Your parameterizations should, as always,be in…

A: abc  d

Q: earch In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated…

A: At 9 am, the time t is 0 hours after 9 am. So, we substitute t = 0 into the function T(t) = 40 + 16…

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Q: Please help me with these questions. I am not understanding what to do. Thank you

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Q: 1.4 points Evaluate the definite integral shown. You must show enough work to convince me that you…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Please help on all asked questions. Pls show all work and steps. Please circle the final answer.

A: Step 1:    Step 2: Step 3: Step 4:

Q: Please help me with these questions. I am not understanding what to do. Thank you

A: Step 1:Step 2:

Q: Find (f^-1)'(1) if f(x )= x/2+sin^2(x) for 0<x<pi/2

A: GIVEN : ​​ STEP : 1 ​​ STEP : 2 ​​  FINAL STEP : ​​

Q: Solve the differential equation. dy 6x2y2 dx

A: If you have any help please let me know in comment box thankyou.

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Q: Solve each problem step by step

A: For g(x):Part (a) Finding the Open Intervals Where g(x) is Increasing:Look at the graph: Starting…

Q: 11. Determine the scalar equation of the plane that contains the z axis and the point P(4,-3,5).

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Q: Find parametric equations for the path of a particle that moves along the circle described by x² +…

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A: For the iterated integral ∫∫∫ dz dx dy, the limits of integration are determined by the boundaries…

Q: Please help me with this question. I am not understanding what to do. Thank you

A: Step 1:   Step 2: Step 3: Step 4:

Q: 43..2 ) Can you please solve this. I am trying to do practice problems to prepare for a test but I…

A: The problem is asking us to find out the time it will take for an investment to double if it is…

Q: Consider the initial value problem. ft(t 2) y+4y= sin(t) \y(1) = 4 The largest open interval where…

A: Step 1:We are given the initial value problem: t(t−2)y′+4y=sin(t)with the initial condition y(1) =…

Q: Q2 (9 points) Calculate SS such that 0 ≤ x ≤ 2π. 1 8x(y-1) dA where D is the region between y = 1 +…

A: Step 1:

Q: 1 Written problems 1. Solve x' 0 1 -1 0 ] x +

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Q: Find the value of the integral: ∬xysin⁡(x)cos⁡(x) dA where the region R lies between the graphs of…

A: Note : • sin(5π)  = sin(2*2π + π) = sin(π)• cos(5π)  = cos(2*2π + π) = cos(π) (Since period of…

Q: Let f(x) = x². Using the Limit Definition, the slope (mr) of the tangent line to f(x) at x = -2 is…

A: We are given the function f(x) = x2 and need to find the slope of the tangent line at x = −2 using…

Q: Q2 (9 points) Find and classify the critical points of the function z = x(2− y)(x + y − 1). That is,…

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Q: Show all steps. Correct flow: -4.5. Correct flux is 4.5

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A: 1. For which values of x is f(x) continuous? f(x) is continuous for x in the interval (-1, ∞) 2.…

Q: Please help me with this question. I am having trouble understanding what to do. Please complete the…

A: Ans page 1:We used the fact : limn→∞​n+11​=0Ans page 2:

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Q: Show all steps. Correct potential function is: f(x,y) = 3xyz +4y +z^2. Correct evaluation gives -39

A: Step 1: Step 2: Step 3: Step 4:

Q: 3 Calculate the integral approximations T and M6 for 2 x dx. Your answers must be accurate to 8…

A: 1. Understand the ProblemWe need to approximate the definite integral of ∫(x² + x) dx from 3 to 5…

Q: Sketch the curve and the approximating rectangles for M 0-1 Esc 12 10 8 2 12 12 10 10 8 8 6 2 -0.5…

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Q: Consider an object moving in the plane whose location at time t seconds is given by the parametric…

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Q: Please help me with these three question. I am having a hard time understanding what to do. Thank…

A: 1) Partial Sum Sequence CalculationsGiven the series:We calculate each partial sum Sn​ as…

Q: 6.2.102. Solve x" — x = (t² − 1)u(t - 1) for initial conditions x(0) = 1, x'(0) = 2 using the…

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