Which of the following is dž for t = 1 if dz dt 2t Z = In(x²y³), x = e¹ and y = e²¹ ? Select one: O None of them e² 08 0 1

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Q: Find the average value of f over the region D. f(x, y) = 6x sin(y), D is enclosed by the curves y =…

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A: Concept: The washer method: The washer method is the name for the use of the slicing technique.The…

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Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

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A: Given: the graph is given we want to find inflection point and concave down range         Inflection…

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A: The Disk Method :  Consider the curve x=f(y) and the y-axis between y=a and y=b and is rotated about…

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A: We need to determine whether each will be a coordinate system or not.

Q: Question 2 i 1: a)' Solve the following linear system in detailed, by using Gauss-Jordan…

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Q: List the first five terms of the sequence. a1 = 3, an+1 = 5an - 5 a1 a2 a3 = a4 = a5 =

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Q: Use the given substitution to express the given radical expression as a trigonometric function…

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Q: √2x+6 2. Y = √√√3x² +10x +3

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Q: Find the radius of convergence, R, of the series. Σ n = 0 R (-1)^_x³n (2n)! Find the interval, I, of…

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Q: Prove the identity. 1+ tan 0 1- tan 0 1- tan 0 =0 19: + To verify the identity, start with the left…

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Q: Question 4 Find r'(t) given the following vector function. r(t) = 2/³i+34j+37²k O r'(t) =…

A: We have to find out derivative

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here, the given curves are: y=1+2x, y=2+x2

Q: 52. If lim f(x) = 6 and lim, g(x) = 3, find x-2 (a) lim [5 f(x) - 4g (x)] (b) (c) lim [4 - xf(x)]…

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Q: Differentiate implicitly to find the first partial derivatives of w. x2 + y2 + z2 - 5yw + 8w2 = 4…

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Q: Calculate the sum of the series Σ n = 5-6(0.6)" 00 n = 1 n whose partial sums are given.

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Q: Prove the identity. 1 + sin x 1- sin x = (secx + tan x)² To verify the identity, work each side…

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A: This question is based on gradient of function at a point.

Q: 2 x³ dx -6 √x²-9 Evaluate O44√3 24√/3 34√5 34√3

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Q: If f is differentiable and ƒ'(x)=x³− 2x² − x+2, then f is increasing on Selected Answers: [None…

A: In this question we have to find interval in which function is increasing.

Q: onsider the following. w=x^2/y ,  x=t^2 ,  y=t+1 ,  t=3 (a) Find d2w/dt2 using the appropriate…

A: Given :w=x2yx=t2  y=t+1t=3

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A: This question can be solved using the concept of partial derivatives.

Q: 9. Determine if the Mean Value Theorem for Integrals applies to the function f(x)=√x on the interval…

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A: Given that, the function is z=c=x2+3y2 and c=0,5,7,9,11,13. For c=0 the function c=x2+3y2 becomes…

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 157 (n + 1)62n + n =…

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Q: F8 e³ti+cos(5t)j +3sin(5t)k 3 -i+cos(5t)j +3sin(5t)k Question 7 The position vector r(t) =…

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Q: Given cos(x)- 글 " what is the value of cos(x +)? 0 O via - IN I 12

A: Given that cosx=12. We have to find the value of cosx+π.

Q: x² - 2x x3 3x² - - dx -In 1x³ 3x² 1 + C Option 1 Option 3 - -In 1x³ 3x² 1 + C In 1x³ 3x²1+ C Option…

A: SOLUTION-

Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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Q: What is the equation of the sphere whose center is at (0, -3, 8) and with a radius of 5? Select the

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Q: Consider the function f(t) = 6 and real number a = - 4. X a. Find and graph the area function A(x) =…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or sin(8n) Σ 47 n =…

A: We will use Ratio-Test to find convergence

Q: V. Provide up to the 5th degree Taylor Polynomial of the given function: f(x)= xex by about x=-1

A: Given :fx=xe-xx=-1

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A: Here we have to write the equation of the curve that passes through the point (1,3) and has a slope…

Q: Find both first partial derivatives. xy x² + y² f(x, y): fx(x, y) = (No Response) fy(x, y) (No…

A: Here we have to find the partial derivative.

Q: S 4x+1 4x² + 2x + 1 dx In 14x² + 2x +1| + C Option 1 In 14x² + 2x + 1] + C 2 In 1 4x² + 2x +11+ C…

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Q: Express the following as a linear combination of u =(3, 1, 6), v = (1, -1, 5) and w = (4, 2, 4).…

A: To write down the vectors into the linear combination of the given vector.

Q: Hallar a de modo que h sea continua para todo ax²-x, x≤-1 ax - 5, x>-1 h(x) =m Envie sus comput X…

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Q: and & and ß are between 0 and f/2. 3

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Q: ections at the given point

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Q: Show your complete solution: Evaluate the triple integral ㅠ pxy 2 L x 0 COS Zdzdydx X

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Q: y' = 2xy²

A: Given: y'=2xy2We need to solve the above differential equation.

Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Given :fx=cotx