Solve the DE. xdygda x² + y² O 2arctan(-) =e- +C ( ² ) = 2e=²¹² + C O arctan -xe-r2 O arctan(-) = --e +C (i)=}e +C ²² arctan

Q: 5 -5 x dx =

A: Topic = Integration

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A: To find length of the curve.

Q: Find the indefinite integral. (Note:USE INTEGRATION BY PART ONLY-Use C for the constant of…

A: We have to find the indefinite integral ∫13 arctan x dx.   Integration by part: ∫u·v dx = u·∫v dx -…

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Q: Evaluate

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Q: Let r(t) (4t+2, -4e¹, 2e #¹). Find the line (L) tangent to r(t) at t = 3. L: (x, y, z) = = +t

A: Given vector:- r→t=4t+2,-4et,2e-4t

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A: Topic - first and second derivative of a function We are given,  y=x5ln(x)we know…

Q: please

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Q: 2 32 32 0-22 3 y=5x-x2 y = x 1 2 3 4 (4,4) G

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Q: For the images attached Find the limit of the following sequences or determine that the limit…

A: NOTE: Refresh your page if you can't see any equations. . find the limit of the sequence

Q: Please solve ASAP. Show your complete solution. 1. The length of latus rectum of a hyperbola is 18…

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A: Let's sketch the graph of functions and find area.

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: The given equation of the surface: 4x2+2y2+z2=15Let, fx,y,z=4x2+2y2+z2-15.

Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = t4 - 18t² –…

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Q: Use a scalar projection (NOT A FORMULA- unless you derive that formula as part of your solution) to…

A: Here we have to find the shortest distance from the point (1,−2,5) to the plane given by…

Q: Find the following using the table below. 1 2 3 4 12 x f(x) 3 4 f'(x) 2 3 1 g(x) 2 1 3 g'(x) 2 3 1…

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Q: = Find a and b so that f(x) is continuous if f (x) = O O a = ¹/2 b 11 a = EE O a= b = 60 7 a = - 96…

A: A function if said to be continuous if its graph has no break on its domain of definition.

Q: x³ Find the absolute maximum and absolute minimum of the function f(x) = - 4x² + 12x - 5 over the…

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Q: For the equation, find dy/dx evaluated at the given values. y² = dy = 8x - 71 at x = 9, y = -1

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Q: -3 2. Express z³+z' (the conjugate of z raised to the third power) in polar coordinated form u(r,0)…

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Q: Given f(x, y) = ry - 6zy. Compute: 8²f dz² 8²f dy²

A: Topic = Derivative

Q: Use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the…

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Q: = 2π/3. Find the directional derivative of f(x, y) = sin(x + 2y) at the point (4, 3) in the…

A: If f is differentiable function then directional derivative of f at the point (p,q) in the unit…

Q: Find 7' (t), given r(t) = (- 4√t, - 3 ln(3t), 3e-³). F' (t) =

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Q: First the pieces: dz dx 8z dy da dt dy dt Use the chain rule to find dz dt || || || End result (in…

A: To find derivative of z.

Q: Below are the polar coordinates. Find the Cartesian Coordinates. (0,5) (-5,0) (0.-5)

A: The polar coordinate is 5, 3π2 We have to convert the Polar coordinate to cartesian Coordinates.

Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

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Q: A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base…

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Q: Given the integral 1 /9 - (x + 2)² dx, king the substitution x + 2 = 3 sin(0) gives the integral

A: Given query is to find the integral.

Q: e Fundamental Theorem of Calculus Part II to find the derivatives of foll (2) = √²* √√₁ + 1³ dt

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 3T…

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Q: |s sin³ 50 √ cos 50 de

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Q: an more work be shown on how to solve this

A: By using a scalar projection to find the shortest distance from the point 1,-2, 5to the plane given…

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Q: Question Determine the interval of convergence for the power series that can be used to represent…

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A: NOTE: Refresh your page if you can't see any equations. . here continuous payment frequency is…

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Q: Use the power series method to solve the given initial-value problem. (Format your final answer as…

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Q: Let f be defined as follows: x 0 f(x) = Which of the following statements are true about? 1. f(0)…

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Q: 4.7.5

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Q: can you please write out the final answer as its supposed to go in the answer box because I cannot…

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Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

A: Given: the radius of a circle increases at a rate of 2m/s. We need to findthe rate at which the area…

Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

A: Given query is to find the interval where speed is increasing.

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Q: A particle moves along the x-axis so that its velocity at time 0 < t < 18 is given by v(t), whose…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)= -2 ex cos (yz),…

A: f(x,y,z)=-2excos(yz) P0(0,0,0) A=-5i+3j+k