1. Solve the following differential equations d²y_dy dx² dx — - +2y=x

Q: b) Use chain rule 1 y= LESANNE aretan u where u eª ue

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Q: Find the general antiderivative of f (x) = 4 x ln x²

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Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

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Q: Evaluate the spherical coordinate integral. 1- cos 2 2π π SS S p²sin & dp do de 00 0

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Q: The vector i +bj-k is perpendicular to the vector I +2j-3k. what is the value of b?.

A: We know that if two vectors are perpendicular to each other then there dot product is zero. Given,…

Q: 6. a) x = -6 b) x = 1 c) x = = /² Determine the derivative of the curve with equation y = 4²x a) 4²x…

A: Given query is to find the derivative.

Q: [ 2² cos z dr = f(z) sin r + g(z) cosz+c The value of ƒ (1) + g (1) is Blank 1

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Q: 1. Given f(x)=x+5 and g(x)=x²+8x+15 Sketch the graph of y=- _f(x) g(x) Mark the asymptote(s),…

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Q: Eliminate the parameter t from the parametric equation x = 3 sint y = 3 cost 0 ≤t≤ 2π.

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Q: find differential equation of the following equation 1) y' = -x y+x

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Q: Consider the function Step 2 of 3: Find lim f(x). x6+ f(x) = lim f(x) = x→-6+ x² + 12x + 22 19x +…

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Q: Power series p₁(x) and p2(x) are given below. P₁(x) = 1 + 7x +49x² + 343x³ +2401x² + ... P2(x) = 1 +…

A: Here, to find the series notations of p1(x)+p2(x)

Q: Find the derivative of_h(x)= (3x+4)³ (-3x-2)

A: NOTE: Refresh your page if you can't see any equations. . take derivative use the quotient rule…

Q: . What is the snortest distance between the parabola y=2x² and the line y=4x-4

A: Shortest distance between two curves are always along the common normal.

Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and concept we will…

Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…

A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

Q: S 2 x² dx x² 2 -9

A: Given,∫x2x2-9dx

Q: Given the following matrix equation, which of the following is the correct matrix solution, A? -5 5…

A: We are supposed to find here matrix addition which we will find as.

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x - 3y - 2…

A: Given: y=√(x-2) , x-3y-2=0

Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: Q1: Find the general solution to the following differential equation: y"-2y'+y=x²-1

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Q: 1. If f(x) = cos²x, then the derivative, f'(x) = ? a) 2sinx b) −2 sin x cosx c) 2cosx d) 2 cosx =…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: T -2 -1 4 3 2 - -3 1 3. From the above graph of y = f(x), find the following limits: (a) lim f(x) =…

A: (a)  limx→-4f(x)=2   (b)  limx→-3f(x)=-2   (c)  limx→-2f(x)=-3   (d)  limx→1f(x)=infinite

Q: In 23 In y SS 10 Evaluate the integral The value is. (Type an exact answer.) ₂x+y dx dy.

A: The given integral,     ∫0ln 23∫0ln yex+ydx dy

Q: dy dx +y = 0 y(0) = 1 Using Power Series, solve for y(x) at x₁ = 0 Using First Order Runge-Kutta…

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Q: Use polar coordinates to find the volume of the given solid: Insider the sphere x² + y² + z² = 16…

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Q: 32) Find the amount of a continuous money flow in which $2000 per year is being invested at 5%,…

A: Given.

Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: 5. If f f(x) dx = 12 and f f(x) dx = 4, then all of the following must be true a. f f(x) dx = 16 ✓…

A: topic- definite integral

Q: 9 The slope of the function ƒ (x) = 8 - 2x is _____. -8 -2 2 8

A: here we have to find the slope of function  so we have to find dy/dx so differentiate the function

Q: et the vector v have an initial point at (-6, -2) and a terminal point at (-6, 2). etermine the…

A: Finding the vector V

Q: Evaluate the following limits: 2. lim G(x) if G(x) = = x →-00 x+61 x+6 2

A: We have to find the limit

Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and calculation we will…

Q: Determine the x - y coordinates of the points where the parametric equation x = 3 sint y = 3 cost 0≤…

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Q: The Taylor series for f(x) = e at a = 1 isen(x − 1)". - n=0 Find the first few coefficients. CO C1 =…

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Q: y = ln x and x-y-4 = 0

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Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 1/3 sq. units 1/4 sq. units…

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Q: 2 problem: it | b₂ b3 2 LG C₂ Cz 201-2 b b 2 46 40 2 5 - 203 bz 3 403

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Q: Integrate (three) of th 1) f sin6x cos3x dx

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Q: + 1 -оу-х -oy=x2

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Q: hav is that not the function defined by ху f(x, y) √x² + y² if differentiable at (x, y) + (0;0) if…

A: We have to show that f(x,y) is not differentiable at (0,0)

Q: y"-y-4e-x+3e2x; y(0) - 0.y(0) --1.y"(0)-2

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Q: 1 Find the first five non-zero terms of the Taylor series for f(x) = - X Written compactly, this…

A: Taylor Series for f(x) centered at x=a is given by f(x) = f(a) + f'(a)1!(x-a) + f''(a)2!(x-a)2 +…

Q: of the points where the parametric equation y = 3 cost 0≤t≤ 2T will have a horizontal tangent.…

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Q: Given the function graphed below, evaluate the definite integrals. 2 3 4 5 6 7 8 -3 -5 [²ƒ(z)dz = −5…

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Q: Q) find differential equation of the following equation dx + x sin(2y) = x cos² (y) dy

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Q: 1- 2- 3- 3-Evaluate the integrals in Exercises: [ sect? (x - 1) dx sech² s sech Vt tanh Vt dt Vt…

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Q: Q) find differential equation of the following equation 1) y' = y-x y+x

A: Solution of the above differential equation is

Q: Determine the number/s at which the function F(x)=√√4x² is continuous.

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the intervals where…

Q: Consider the following function: f(x) = - -x4 + 2x³ +6 Step 2 of 4: Determine where the function is…

A: Here is the solution: