If F = (x²)i + (2x²y)-(3-2)k find div f curl f at (1,-1, 1).

Q: the function. 4) ((x) = fx+3, for x>0 [x², for x ≤0

A: Given above function is x+3, for x>0x2, x≤0

Q: In(y) = −3x² + ln(7)

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Q: The value of the following limit Lim (cos(x) cot(x) is: AL

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Q: A radioactive substance decays in such a way that the amount left after t years is given by A=100e…

A: Follow the procedure given below.

Q: Psychologist L. L. Thurstone suggested the following relationship between learning time T and the…

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Q: Consider the following. x² f(x) = x + 7 Find the derivative of the function. f'(x) = x(x+14) (x+7)²…

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Q: Find dy /dx for the following functions: -) y².cotx= [sin(x. y)]-¹ b) y = (lnx+x) tan x

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Q: 2 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x =…

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Q: (i) Find the shortest distance from the origin to the line 3x + y = 6 and give the coordinate of the…

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Q: 33. " +9y sin 2x; y(0) = 1, y' (0) = 0 34. y" + y = cos x; y (0) = 1, y'(0) = -1 35. y" - 2y + 2y =…

A: Given: y(3)-2y''+y'=1+xexAuxilliary equation: m3-2m2+m=0Therefore, m=0,1,1Complimentary…

Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y =S₁ dx (x-1)².…

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Q: x-8 7 Consider the lines 1₁: x = 1 + 3t, y = 2 + 3t, z = 3 - 10t and 1₂: a) Find the point of…

A: Given problem:- Consider the lines l1 : x = 1+3t, y = 2+3t, z=3-10 and l2: (x-8)/7 =(y+1)…

Q: Solve for t, 0≤ t < 2π 18 sin(t) cos(t) = 12 sin(t) t = Give your answers accurate to at least two…

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Q: Sketch a graph f(x) = 2 sin [-2(x+1)]-3 for two cycles. ✔✔✔ 5. List 3 key points below. >

A: Concept:  The sine function's general form: y=Asin(Bx-C)+D Where A represents the amplitude Period:…

Q: Identify the surface defined by the following equation. 2x-y²-z² =0

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Q: Use long division to divide. (Simplify your answer completely.) (8x237x - 15) + (x - 5) X = 5

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Q: 7. A line has equation /:*-=-= 1:*=1==32₁2=3 x-1 y-2 -,Z=3 z a) Write the parametric equation for…

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Q: Solve the given initial value problem. x³y² - y³ = 45 ³y² + xy³ = 18 x²y² + xy³ = 90 x¹ y² + y² =…

A: Here we have to solve the differential equation.

Q: Q2. Find the angle between the vectors and .

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Q: For the three-part question that follows, provide your answer to each question in the given…

A: We will compare given equation with y=aCosbx-c+d

Q: Graph the rational function. -5x-15 f(x)=- x²+2x-15

A: Graph the rational function :      f(x)=-5x-15x2+2x-15 Start by drawing vertical and horizontal…

Q: For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line r = (2,−1, −2) + t(3,1, −2)…

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Q: Evaluate the integral: LIVE 1 I√9r²+25 dr.

A: We will solve the given question using simple Integration rules.

Q: By using the unlimited coefficients method, choose the correct answer for this equation…

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Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: 5. Given that, the points are 1,3,0 and 2,4,4. Note that, the symmetric equation of the a straight…

Q: 3. Evaluate f sin(3x - 1) dx

A: we want to determine the integral  ∫ sin(3x-1) dx

Q: /sin-¹ (√x) dx tegral.

A: Let I=∫sin-1x  dx

Q: Consider the following function. Function f(x) = 8x4 - 6x³ - 165x² - 37x + 60 (a) Verify the given…

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

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Q: 10. Solve each of the following systems; a) 2x+3y-z=-2 x - 2y + 3z=13 4x + y + 3z = 9 c) x + 2y + 72…

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Q: The growth rate of a town's population after t years is P'(t) = 420 t². If the town's current…

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Q: Helicopter Task Introduction: An observer at Point A makes measurements that show that the peak of…

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Q: For the following equation, find x. 2 log bx= log9+ log125-log 15 (Type an integer or a simplified…

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Q: Find the open intervals where the function graphed below is (a) increasing, or (b) decreasing. Ay…

A: Consider the graph

Q: Use the following equation to answer the questions: y = 4 cos (1/₂) 4 Find the period Find the…

A: Explanation of the answer is as follows

Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: find the area of the region bounded by the curves 4x - y2 = 0 and y = 2x - 4

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Q: 9. Determine the Cartesian equation of the plane that contains the intersecting lines: -2 y 2+3 x-2…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: topic- average value of function over interval

Q: Find the vertical shift of the sinusoidal function. fx -3πT -2T Simplify any fractions. T 6 5 ★ تلا…

A: Concept: The sine function's general form: y=Asin(Bx+C)+D The vertical shift: This is the vertical…

Q: Q6) Find the Area bounded by the curves y = √√x and x = 2y-y² ,with sketch.

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

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Q: A function f(x) is continuous on the real numbers and has the following features about the point x =…

A: This question is related to Functions, we will solve it using given information.

Q: Find the area of the region between f(x) = x² + 2 and g(x)= x - 1 on the interval [-2,2]

A: The functions are f(x)=x2+2  &amp;  g(x)=x-1

Q: A baker sells cupcakes and bases her prices on the number of cupcakes purchased. 72Total Cost 66 60…

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Q: Find x in the following equation. log 10 (x+1) - log 10 (x-1)=1 (Type a fraction or an integer.…

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Q: Sketch a graph of f(x) 5 4 3 2 1 -5 -4 -3 -2 -1 - 1 { 0 if x ≤ - 2 x + 1 if -2 2 2 3 4 5 Open Dot…

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Q: 1) Write a differential equation that models this situation. Let V represent the volume (in gallons)…

A: Note: as per guidelines we support only three subparts of the questions.kindly repost next…

Q: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A: A tank contains 160 liters of fluid in which 10 grams of salt is dissolved. Pure  water is then…