Solve: xy + y + 4x³y¹ = 0 O 6ry³ + Cr³y³ = 1 O 15r y³ +Cr³y³ = 4 O9r³y³ + Cr³y³ = 5 O 2r³y³ + Cr³y³ = 1

Q: What is the general solution to the the differential equation 3y''-y' - 2y=0? (2/2)

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Q: 1/5 a) S J1/10 10 Arc sin(5x) dx

A: Please see the below picture for detailed solution.

Q: 5. Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and…

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Q: 6. x³-x²-x+10 lim x-2 x² + 3x + 2

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Q: у 7. y' +²√y = 0, y(1) = 0 - x

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 2x² + 5y², the planes * = 5…

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Q: so xe x dx

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Q: In the below series find the missing noumber  2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

A: Given data:- The below series is given, 2 , 3, 6, 11, 20, 37, 68, 125, 230, __ , 778,1431

Q: Let E be the solid below z = 50- x² - y² and above the square [-5, 5] × [-5, 5] Given the solid has…

A: Let's find moment of inertia of E about z axis.

Q: 5. (a) Suppose a particle moves along a trajectory given by the vvf r(t). If its veloc- ity and…

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Q: Let f(x) = ln(x² + 2x + 6) f'(x) =

A: We have to find the derivative.

Q: Consider the vector whose initial point is P(-6, 6) and terminal point is Q(5, 3). Find the position…

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

Q: Set up the definite integral required to find the area of the region between the graph of y = 13 –…

A: Concept: Area between the two curves: Let y=f(x) and y=g(x) be the curves and a and b are two…

Q: Consider the following function. f(x) = (x-8)ex (a) Find the critical numbers of f. (Enter your…

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Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

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Q: 1 Find the Taylor Series generated by f(x) = (7-X)⁹ at X=6 9 (7-x) 10 f'(x) = 90 f"(x) = (7-x)" f(x)…

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Q: Consider the function f(t) = 5 sec²(t) — 9t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: SEND IN 20 MINUTES PLEASE !!!! Find all extreme points (maxima, minima, saddle points) of…

A: Extreme points of the function fx, y=2x3 + 2y3 - 9x2 +3y2 - 12y

Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

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Q: Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any…

A: Given: rt= cost i + et j + t2 k

Q: In this question, consider the vectors 10 8 V1 ~- - ( ) - ~- - ( ) - - - () ---- () v2 = V3 = b and…

A: The objective of the question is determine the coefficient matrix" A" without simplifying.

Q: 2. Compare the rates of growth of f(x) = x + sinx and g(x) = x as x approaches infinity. f(x) grows…

A: The given functions are fx=x+sinx and gx=x we have to compare the rate of growth as x approaches to…

Q: 3. Evaluate f(x) = 15 – ½ (x) for f (4). a) 16 b) 14 c) 13 d) none of the above

A: 3.  This is a problem of polynomial.  Here given a polynomial f(x) and find f(4).

Q: Find the speed of the object whose position function is given by F(t) = (4t² - 1, 4t - 2, t³ + 6t)…

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Q: X A company manufactures mountain bikes. The research department produced the marginal cost function…

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Q: 5 ΣΕ j=1

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Q: Find the area of the region between y = 6x² and y = x² + 7.

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Q: The differential equation dy x-2y+3 ax 2x+3y-4 = is reduced to [homogenous or separable

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Q: Solve the differential equation (1 − xy)−²dx + [y² + x²(1 — xy)−²] dy + x²(1 − xy)−²] dy = 0; y (2)…

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Q: Question 3 Evaluate the limit. Hint: Factor and enter decimal answer. x + 3 x-3 x² + 8x + 15 lim

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Q: How do I find tangential and normal components of the acceleration, from question 5b

A: Let's find tangential and normal components of acceleration.

Q: 5) Show that to order O(h²), the central difference formula for the partial derivative მ3u(x,t) əx3…

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Q: əz 7. Find the partial derivatives and if: əz əx ду (a) z = x-y r2 + 1² (x, y) = (0,0) = x² sin(x-y)…

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Q: Find (3x + y)dA where D = {(x, y) | x² + y² ≤ 16, z ≥ 0} Round your answer to four decimal places.

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Q: 2 (2y² + 5xy 4 Ο α. χ' (y² + 2xy = y + 2) = C O b. x4 (y² O 2y + 4) dx + x (2x + 2y − 1) dy = 0 - -…

A: The given differential equation is; 2(2y2+5xy-2y+4)dx+x(2x+2y-1)dy=0.

Q: Prove that the given transformation is a linear transformation - ( ) T: R³ R³; Ty = x+y+z/ + y

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Q: Q4. Find the values of the constants a, b, c so that F = (axy + bz3³)ī+ (3x² - cz)j + (3xz² - y)k is…

A: Note: According to our expert guidelines only first individual question is to be answered kindly…

Q: Find the area of a triangle PQR, where P = (-1,-1, 1), Q = (4, -3, -6), and R = (1, -6, -3) Check…

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Q: What is the general solution to the the differential equationy'''=0? A y=C₁+C₁₂x 1 By=C₁+C₁₂x+C₁₂x²…

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Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

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Q: Answer: Use a triple integral to find the volume of the solid enclosed by the paraboloids y = x² +…

A: Let's find volume by using triple integral.

Q: Consider points A(4, -1, 3), B(3, 1, 6), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

A: The given problem is solved below in detail.

Q: Differentiate the following function. You do not need to simplify the derivative. h(x) = 2x²ellz…

A: Topic = Derivative

Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

Q: Find the second derivative of the vector-valued function r(t) = (4t+ 3 sin(t))i + (5t + 3 cos (t))…

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Q: Sketch a graph of a continuous function f with the following properties: (i) f(x)=0 for x = 0 (ii)…

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Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: If C(x) = n=0 ∞ n=0 2n + 1 2n + 2 2n ²n and S(x) = ∞2n+2 2n + 3 n=0 -x²n+ find the power series of…

A: The given power series, Cx=∑n=0∞2n+12n+2x2n and Sx=∑n=0∞2n+22n+3x2n+1

Q: 5. (y4 - 2xy) dx + 3x² dy = 0; when x = 2, y = 1.

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Q: Let f be a continuous function such that -6 [', f(x) dx = 9. What is the value of -3 f(x) dx = -10…

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