Part III. Evaluate the following. Justify each step if necessary. 1. If F(x)= [mm (8-) √²+3 dr. F' (1). tan

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Q: i) Consider the double integral I = -ff₁₂² Le e²² dx dy. y/3 Draw the region of integration then…

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Q: Question 4. Continuity Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x =…

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A: Use trigonometric coordinate syste

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A: Given matrix, A=0000-90002000-7000400050000

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A: Given, ∫125+x2dx

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A: Given, r(t)=&lt;5t4-5,-e2t,-3sin(3t)&gt;

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Q: Determine the absolute extrema of the given function on the specified interval. Show your solution…

A: Please see the below picture for detailed solution.

Q: Determine the absolute extrema of the given function on the specified interval. Show your solution…

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Q: both answer are not correct.

A: Let's find beam of light moving along the shoreline.

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A: Given problem:- A lighthouse is located on a small island 4 km away from the nearest point P on a…

Q: 4. Given f'(1) = 4, g'(1) =— 2, ƒ(1) = 1, g(1) = 1, find h'(1) if h(x) = xg(x)+7 f(x)

A: Using definition if derivative of f/g

Q: E) If F(x, y, z) = 3x²i + 3zj - 3xk find the Div (Curl F). 0/0 0/0 0/0= az any jaz V-Vx3 = 0₂ 17 Pue…

A: First we find curlF .

Q: Solve the following integrals: 1. S-7e*dx 2. (2ex - 6x) dx √² (3x) dx 3.

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Q: (5)  Please explain in words how a student would determine the normal vector to the direction vector…

A: explanation of determination of normal vector are as follows

Q: Nx - My If = R, where R is a function depending only on the quantity z = xy, then the differential…

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Q: non-permissible values of x for the identity cscxtanx=secx are?

A: non-permissible values of x for the identity cscxtanx=secx are?

Q: Q2: write and prove an Approximation property for the Supremum.

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Q: Let r(t) = Find fr(e) de (don't include the +C) fF(t)dt = < [

A: Given,  r→(t)=-4t4-3,-4e3t,-2sin(-t) ∫r→(t) dt =∫-4t4-3dt,∫-4e3tdt,∫-2 sin-tdt

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Q: d. What are the intervals of concavity? e. What are the x and y-intercepts? f. Are there any…

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Q: 3. Evaluate the indicated line integrals in the complex plane by direct integration. Siz dz along…

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Q: Explain why the function is differentiable at the given point. f(x, y) = 9+ x In(xy-7), (2, 4) xy…

A: The linearization of a function f(x,y) at (x0,y0) isL(x,y)=fx(x0, y0) (x−x0)+fy(x0, y0)…

Q: Solve the following x³-x²-√√2x limx→2²-11x+18

A: Above question is solved.

Q: Find 넥 L -TS (s+1)e- s² + 4s + 4

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Q: Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: Solve by Cramer's rule. X1 i X2¹ 6x1-2x2=4 3x1 + x2 = 10

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Q: Consider the following: a. Write an equation of a plane in Cartesian form that contains the point…

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Q: The rate of growth of the population of a city is predicted to be the following, where p is the…

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Q: 2) Carbon-14 decays or emits a radioactive particle at a regular and consistent exponential rate and…

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Q: An angle co-terminal to 19 6 11m 6 is

A: Given query is to find coterminal angle.

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Q: 1) Solve the following equations for x: a) 2e6x = 18 b) = 1 c) 2* = e5 e +²

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Q: Question 1 of 14, Step 2 of 3 1/20 Correct When a factory operates from 6 AM to 6 PM, its total fuel…

A: Given query is to find rate of consumption at 10 AM.

Q: Evaluate the following integral using trigonometric substitution. 36x² - 49 7 S² dx, x> 3 x³ 2 √36x²…

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Q: 1. The graph of y=sin z is transformed so that the transformed image has a period of 4m and a phase…

A: Given problem:- The graph of y = sin x is transformed so that the transformed image has a period of…

Q: II. Solve the initial value problems given the following: dy 2 if y(-1) = 21. = -2x + 3x dx dy -2x…

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