Number 2: Given the following first-order linear differential equation: v-1 dv 32 dt V e Write the given first-order LDE in standard form

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: See this solution in below.

Q: Use the tangent plane to approximate a function of two variables at a point. Use a tangent plane at…

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Q: 42. The term that does not contain x in the expansion of 8x +

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Q: Given the position function s(t) = 2+³ - 2 +² - 60++ 3₂ where it is in seconds and s is in ft, Find…

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

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Q: 9 8- 7 16 1 A 3 يها 2 1 If f(x) f'(3) = = g(x) g(x) h(x)' 2 3 x-values then 5 4 يها 2 1 h(x) 1 2 3…

A: Given that graph of gx and hx    and fx=gxhxTo find :f'3Solution…

Q: (a) Find the dy = differential dy. y = ex/2

A: We will use differentiation to solve this.

Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: Show that the triangle with vertices A, B, and C is a right triangle. d(A, B)2 = 145 d(A, C)² + d(B,…

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Q: (a) Using your calculus skills, find the equation of the tangent line to the parabola y = 4x² - 2x +…

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Q: Differentiate. f(x) X x+ C X

A: Topic -Derivative of a function We are given, f(x)=xx+cxwe know thatddxuv=vu'-uv'v2    [ u and v are…

Q: Using the shortcuts for finding a derivative to find the derivative of 17 √x f(x) = 7√x f'(x) =

A: Topic = Derivative As per guidelines , at a time only one question can be answered. please repost…

Q: Differentiate y = ex+2 +9.

A: Given function is y=ex+2+9 We need to find the first derivative of the given function.

Q: Consider the function of two variables f(x, y) = 3x³9x + y² + 4y + 6 (a) Find all the critical…

A: Consider the function of two variables fx, y=3x3-9x+y2+4y+6 a To find all the critical points of fx,…

Q: 16² - 15 $+

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

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Q: Consider the ellipse foci? (x-5)² 256 + (y-7)² = 1. From any point on the ellipse, what is the sum…

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Q: Let r(t)= (212-t,t³ +1²-5t), -2≤t≤ 2. (a) Sketch the curve which is generated by r(t). You may use…

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Q: Find an equation of the tangent line to the curve at the following point: y = (1-3x)¹0, (0, 1)

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Q: Complete the description of the plecewise function graphed below. S 1333. { f(0) = ( { O Question…

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Q: Question 2 Let f(x, y) = 5e¹* sin(3y) af д х af dy =

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Q: Determine the derivative of ln(csc) CSC I POMOSOME CSC I O - cot a Ocot z

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Q: Find the integrating factor (3x²y-x²) dx + dy=0 Select one: 0 а. ex O b. O C. e-x² Od era O e.

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Q: Which of the following is the correct form of the partial fraction decomposition of OA.1 + B. 1 + L…

A: The objective is to find the correct form of partial fraction decomposition.

Q: 5 Find the center and radius of the circle. Write the standard form of the equation. The center of…

A: We know that the centre is the mid point of diameter.

Q: A series circuit has a resistance R = 10 Ohms and inductance L = 2. The battery gives a constant…

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Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4321 per…

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Q: dr Solver +rsece = cose Select one: O a r= O b. r= O c r Od r O e r= 20 - cose + c seco - tane 0 +…

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Q: Find the parametric equation for the line where the planes 4x + 6y + 2z 12 and 2x - y + z = 2…

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Q: Calculate the partial derivatives of a function of two variables. Given f(z, y) = 10 + 4y + 7zy,…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Let a = (9,5) and 6 = (5, -3). Compute the following vector projections. proja b projz a =

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

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Q: The

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Q: Given f(x, y) = x¹ + 5x²y³ – 5y6, find 4 fz(x, y) = fy(x, y) = fxx (x, y) = fxy(x, y) =

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Q: 2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the…

A: Given data:- The given differential equations, (a); 2t2y''+ty'-3y=0,       y1t=t-1 (b);  4x2y''+y=0,…

Q: Which of the is the best transformation of f trigonometric substitution? Of sec 0 de Of 5 sec 0 de O…

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Q: Differential Equations d³y(t) ·x(t) dy(t) + y(t) = 0 dt³ dt Linear or Non-Linear Constant or…

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

Q: 28. (2A + B²)4

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Q: Find three positive numbers whose product is 86 such that the sum of their squares is as small as…

A: Let the three numbers be x, y and z. x + y + z = 86 -----(1) ⇒ z = 86 - x - y ------(2) Product, P =…

Q: S x² x²+49 -dx

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Q: Applications of Planes in Space Find the acute angle (in degrees) between the planes - 2x - 4y + 2z…

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Q: Find the distance from the point (-2, 8, 9) to the line ā(t) = ( − 1, 3, 2)t + (− 2, 3, 9).

A: To find the distance from the point -2, -8, 9 to the line a→t=-1, 3, 2t+-2, 3, 9.

Q: This is incorrect. Please resolve.. UPVOTE WILL BE GIVEN

A: The given answer is not incorrect it is just incomplete. Will be providing the complete solution in…

Q: 6 5 4 3 2 -6 -5 -4 -3 -2 -1 lim h→0 -2 -3 -4 -5 2 3 4 y = g(x) is graphed above. Estimate the…

A: Given query is to find the value of the expression.

Q: Consider the ellipse A. (-5,1) (x-5)² 256 (y-7)² 400 B. (-5,-1) 1. One of the foci is at (-5,15). At…

A: Given equation:- x-52256+y-72400=1

Q: Given that f(x) = x¹²h(x) h(-1) = 2 h'(-1)=5

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Q: Find Vectors and Perform Vector Operations in R³ Find a vector with initial point ( – 2, 5, 0) and…

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Q: I need the P prime and Q prime of 1 and 6 P'(1)= Q'(1)= P'(6)= Q'(6)=

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Q: b) For each of the following, let A and B be some sets, both subsets of universal set U = {x|x is an…

A: Please see the below picture for detailed solution.

Q: Evaluate: fx In xdx X ○ 25 (In x-²) 5 25 (In x-1) 5 + C O 25 (In x+²) 5 + C O None of these + C

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