Let y = 3e¹ 2x³+e-4z. . Which is y'? You will need to simplify to find the answer.

Q: Compute the line integral f(x² + y)ds, where C is the arc of the circle x² + y² = 16 In the second…

A: To find The line integral, where C is the arc of the circle

Q: Let f(a, b) = a/ (b − 1)^2 . a. Describe the domain of f. b. Sketch the level curves of f…

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Q: Find all exact solutions on the interval 0 ≤ 0 < 2. If there is more than one answer, enter them as…

A: Given that the equation we have to find the exact solution of the given equation

Q: Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 5 by…

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Q: Find the standard equation of the sphere with the given characteristics. Center: (-1,-9, 5) Radius:…

A: To find the standard equation of the sphere with the given characteristics.

Q: 1. y'(t) − y(t) = 1, Ans. y(t) = e' - 1 y(0) = 0

A: given IVP

Q: Use Green's Theorem to evaluate the following integral, S (et² +24y³) dx + (8y5 – 24x³) dy where C…

A: We have to use the green's theorem

Q: Find 3838 Əw Əv Əw - Əv y when u = 0, v = 0 if w=x² + −, x=3u - 6v + 1, y = 6u +3v - 3. |u= 0, v = 0…

A: Find

Q: 2. Find the Wronskian of the following: b) (sin cos

A: We have to find the Wronskian for the given function.

Q: e. Σ n=1 (-2)n-1 √n

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find a general solution of the system x'(t) = Ax(t) for the given matrix A. -96 4-[-] A = - 15 9…

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Q: Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b) and…

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Q: Consider the following line integral over the given plane curve. Use x as the parameter to write…

A: Consider the line integral

Q: Find the total differential U=-2t tan(7st)

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Q: -4 -3 f(x) dx = 2 f(x) dx = -2 π 7 4 (a) Use the figure above to find the value of the integral. 3…

A: Consider the graph

Q: 1. The value of a parcel of land bought for speculation is increasing according to the formula t1/4…

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Q: Find the antiderivtive: /102³-52² +7 x6 -dx = + C

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables x, y, z)…

A: The given plane equation is To find:- The limits of integration

Q: (a) Use the figure to find the [ f(x)dx. -3 value of VA f(x) dx? L²₁ f(x) dx = = -10 (b) If the area…

A: Question No. part (b):If the area of the shaded is , then to find .

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 4! 1-3-5-1-3-5-7…

A: The ratio test states that

Q: Find the area under the graph of f(x) = x² + 10 between x = 0 and x = Area = 6.

A: Givenf(x) = x² + 10x = 0 &amp; x = 6

Q: Find the relative rate of change of f(x) = 12 +2e-2x The relative rate of change of f(x) is

A: The objective of this question is to find the relative rate of change of the function f(x) = 12 +…

Q: Find the work done by the force field F in moving an object from P(-7, 7) to Q(7,5). F(x, y)-i-j

A: Let a force field is given as, F= ai +bj and to find the work done in moving the object from a point…

Q: Verify Green's Theorem by evaluating both integrals an √ 7² dx + x² dy = √ √ √ (²x- ax for the given…

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Q: 3. Let F(x) = sindt. (a) Show that F(x) = x −· 3.3! 5.5! 7.7! + by integrating an appropriate power…

A: The objective of this question is to express the function F(x) = sin(x) as a power series and then…

Q: A stone is thrown from the top of the building. It's height (in feet) above the ground after t…

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Q: If n is a prime number greater than 3, what is the remainder when n² is divided by 12?

A: The objective of this question is to find the remainder when the square of a prime number greater…

Q: Find the volume formed by rotating the region enclosed by: 3 6.9y and y = x with y ≥ 0 X = about the…

A: given function

Q: Əw Əv y Find when u = 0, v = 0 if w=x² + Əw Əv |u= 0, v = 0 " x=4u-2v + 1, y = 2u + 6v - 1. =…

A: Consider

Q: LESSON 15: HOMOGENOUS SECOND ORDER LINEAR DE 1. Given c) Solve the IVP if d) Solve the IVP if y(0) =…

A: The given differential equation is

Q: (b) O Σ -1/2-²0 6 n=1 Sn Sn 10 4 n Sn 7.8749 2 4 5 n 6 X .... 6 8 7.8750 ... 8 10 10 10 X Sn Sn 3-…

A: Given series

Q: For which positive integers k is the following series convergent? (Enter your answer as an…

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Q: Find the first partial derivatives of the function z = (2x+6y)¹2. dz dr 1. 2 dy

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Q: Evaluate the integral: | 28x² 49 - x² -dx

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Q: g(b) Use the Substitution Formula, f(g(x)) • g'(x)dx= f(u) du where g(x) = u, to evaluate the…

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Q: Let T be a linear transformation induced by the matrix A = Find the matrix of T-¹.

A: The given matrix is,A=(4−32−2)Find the determinant of the matrix…

Q: Problem #4: When a 5 kg mass is attached to a spring whose constant is 20 N/m, it comes to rest in…

A: We have to find the position of mass when t= and amplitude after a long time.

Q: Use Newton's method to estimate the two zeros of the function f(x)=x-x-2. Start with x= -1 for the…

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Q: fx csc x² c X CSC csc x² cot x² dx

A: +C

Q: 2) Sketch the appropriate region and find the exact area between the curves y y = and y=0, x=1, x=9

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Q: Compute the directional derivative of the following function at the given point P in the direction…

A: To Compute the directional derivative of the following functions at the givenpoint P in the…

Q: But Use analytic methods to find (a) the critical values, (b) the local extrema, (c) the intervals…

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Q: What is the unit sphere's equation in spherical coordinates? p=1 2 p² + 0² +6² = 1 p=2 cos p p = 2…

A: The objective of the question is to identify the correct equation for a unit sphere in spherical…

Q: (-1)" « * Σ(n+1) (c) n=1

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Q: OPTIMAL INVENTORY STRATEGY: An office supply store expects to sell 1380 units of a specific model of…

A: An office supply store expects to sell 1380 units of a specific model$6 per printerThe fixed…

Q: Given that f(x)=√x-5 and g(x)=x+1, what is the rule and domain for fog)(x) Only one item from the…

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Q: A triangular plate with height 6 ft and a base of 8 ft is submerged vertically in water so that the…

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Q: True or false: If f is a differentiable function, then [ƒ(√)] = d dx f'(x) 2√x

A: To determine whether the following statement is true or false.If  is a differentiable function, then…

Q: Find two positive numbers that satisfies the given requirements. The product is 147 and the sum of…

A: To find two positive numbers that satisfies the given requirements.The product is 147 and the sum of…

Q: Ans. y=10 cost + 2 sint-√√2 sin√√2t 5. 2y+3y"-3y'-2y=e', y(0)=y'(0) = 0, y"(0) = 1 8 1 Ans. y 9 -1/2…

A: 2y'''+3y''-3y'-2y=e-t, y(0)=y'(0)=0, y''(0)=1