question: 2. xdy + (xy - y - y²) dx = 0 answer: 2.y = x Cex+1

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Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

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Q: Find the directional derivative of f at the given point in the direction indicated by angle f(x,y)…

A: Given function is: f(x,y)=excosy We have to find the directional derivative at the point (0,0) in…

Q: Calculate the directional derivative direction Q(5,4) 4 3√-3x²-5xy3 of at P (1,-2) in the

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Q: a) b 5. c) [ 4x²-3x+2 dx. x Evaluate f Solve the initial value problem = cost-2 sint, z(0) = dt Find…

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Q: f(x) 3. What does lim = 0 show? X→∞ g(x) O g(x) grows faster than f(x) as x goes to infinity. Of(x)…

A: The given limit is limx→∞fxgx=0

Q: Evaluate: (In x)² x -dx - +C

A: Topic - indefinite integral ∫xndx=xn+1n+1+C

Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

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Q: Which function has Maclaurin series (-1)"2""? n:o OAI OB 8. 2/7/2 Oc O D. TIZE D.E. 2

A: The given series: ∑n=0∞-1n2nxn

Q: sin(x - a) lim x→a 2(x²-a²)

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Q: Determine the general solution of xdy + ydx = 0 A xy=c B) xy^2 = c y=c (D) X=C

A: Given Problem:- xdy+ydx=0 Find General equation  of given differential equation

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: Let v = 37 - 47 + 2k. Find ||||. Check Answer

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Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

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Q: For the following exercise, find the volume generated when the region between the curves is rotated…

A: I am attaching image so that you understand each and every step.

Q: A Law office has 20 files awaiting transcription. The legal secretary has been able to complete 2…

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Q: IN 10 MINUTES PLEASE JUST WRITE THE ANSERS NO DETAILSSSSS!!!!! Let f(x,y) = xsiny + ysinx +xy be…

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Q: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

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Q: Find the average value of the following function where 9 ≤ x ≤ 11: f(x) = X C 81 dx

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Q: Given f''(x) = 7x - 2 and f'(0) 2 and f(0) = 1. Find f'(x): and find f(4) =

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Q: Consider lines L₁ and L₂. L₁: x = 1 + t, y = t₁ z = 2 + t, t€ R, L₂: x-3=y-1=z - 3 (a) Verify…

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Q: Find the equation of the tangent to the curve y = sin(3x) COS(z) at z = 4.

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Q: sec 2(t)- 9t2 Justify your response. b. Find the antiderivative of f(t) = s

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Q: Find the arc length (s) of the curve (t) 8 = r(t) = (5e³t, 4e³t, 2e³t) for 0 ≤ t ≤ ln(4)

A: The arc length s of a curve r→t = xt, yt, zt for a≤t≤b is given by s = ∫abx't2+y't2+z't2 dt

Q: Find -(62). Type In(x) for the natural logarithm function. da

A: Topic = Derivative

Q: SEND IN 20 MINUTES PLEASE !!!! Find the absolute max. and absolute min. values of f on the given…

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Q: , b) Find the angle ZB.

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Q: Using calculus, find the absolute maximum and absolute minimum of the function f(x) = 7x² − 14x + 4…

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Q: a) Use the Newton-Raphson method to solve the following equation for x to six decim x - ln x=8 (Use…

A: Here we have to use the Newton's raphson method

Q: Below is the graph of y = x² +5. 141 12- 10 -2 -1 8- 6- 4- 2 0 1 2 3 The area bounded by y = x² +5…

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Q: State whether the given sums are equal or unequal. 20 20 Aj and ke j=1 k=1 O Unequal O Equal > Next…

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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. Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y)…

A: At first we derive second order partial derivative of the given function   f(x,y)=yFxy.

Q: 2. Solve the differential equation dx for y = f(x) with the initial condition y(0) = 2.

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Q: Evaluate the definite integral 8 6x² +6 -dx

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Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: face da +C

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Q: 2. A force F = [-2,1,5] in Newtons, pulls a sled through a displacement s = [-3, 5, 4] in metres.…

A: Using dot product of vectors and obtain the magnitude of the force vector

Q: Evaluate f 4x²-3x+2 X dx.

A: Given, ∫4x2-3x+2xdx

Q: 1. Conisder the vvf r(t) = 12ti — +8t³/2 j + 3t² k, t> 0. (a) Find the arc length of the curve for…

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Q: Differentiate the following function. You do not need to simplify the derivative. f(x) = (In x)5…

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Q: The demand for a certain product is given by the function D(q)= −2.1q+350 where q is the quantity in…

A: Given, The demand for a certain product is given by the function D(q)= −2.1q+350 where q is the…

Q: Find all the values of x such that the given series would converge. ∞ (-1)" Σ (x¹)(n+3) (5)" n=1 The…

A: answer is in next step. please give a like !!

Q: ✓ ["1 [™ f(a)da - [* f(x)dx = - Sª f(x)dx and b where a = If what are the bounds of integration for…

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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: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given: ∫05|10x-5|dx

Q: If f(x) = (t + 3)e' dt, on what interval is f increasing? (Justify your answer)

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Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

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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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