= Set up the definite integral required to find the area of the region between the graph of y y = 2x + 17. J dx T² - 18 and

Q: y" - y'-12y=6sin (2x)

A: Given problem:- Solve y'' -y' -12y= 6sin(2x)

Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (5, -3), vertex…

A: The general form of the parabola is given by: y=a(x-h)2+k...(1) where (h,k( is the vertex of the…

Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?…

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Q: b Prove that: f(x) dx = F(x) =F(b)-F(a)

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Q: Find the Maclaurin series and corresponding interval of convergence of the following function. f(x)…

A: Let's find.

Q: Find the limit. Use l'Hospital's Rule wher lim [In(x⁹ – 1) – In(x³ – 1)] - - *-1*

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Q: Evaluate the line integralſ (x+2y) dx + x² dy, where C consists of line segment from (0, 0) to (2,…

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Q: The length of each of the two equal sides of an isosceles triangle is 24 meters (see figure). The…

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Q: Evaluate the following indefinite integrals using integration by trigonometric substitution.…

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Q: Representing a function as a Power Series. Suppose that we want to represent the function f(x) =…

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Q: Solve for the solution of: (D3 + D)2y = 0

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Q: Prove the identity. COS X 1-sin x 1+ sin x COS X Note that each Statement must be based on a Rule…

A: Solution )  cos x / ( 1 - sin x ) Multiply cos x in numerator and denominator =cos x × cos x /  […

Q: Describe the graph of the equation. r = 3 sin 16t i - 3 cos 16t j O It is an ellipse in the…

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Q: Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED. log₁ (x+3) lim x →1 -1 1-cosh…

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Q: Suppose that f(x) and g(x) are given by the power series f(x) = 6+7x+7x² + 4x³ +….. and g(x) =…

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Q: 5. S COS X 2+3sinx dx

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Q: If f(x) = 6 + 6x - 2x², find f'(-3).

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Q: Replace the polar equation with an equivalent Cartesian equation. r² = 44r cos 0 (x-22)² + y²-0…

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Q: 3. Evaluate the line integral Sc F. dr where F(x, y, z) = (e², xz, (x + y)) over the curve r(t) = t²…

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Q: 2 Find az/ax if the equation yz - Inz = x + y

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Q: For F(x, y, z) = (x + yz) i + (y + xz)j + (z + xy) k, find: (a) the curl (b) the divergence

A: To find curl F and div F

Q: Find a general solution. Show the steps of derivation. Check your answer by substitution. -1.2 6. y'…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: Cos(c+d) = Cosc.Cosd - Sinc.Sind  Sin(c+d) = Sinc.Cosd - Cosc.Sind

Q: Find a vector parametrization of the ellipse centered at the origin in the xy-plane that has major…

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Q: Evaluate the line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: Given: xy =tan(x - y). Find dx/dy. tan² (z-y) soc²(z-v) +tan² (z y) sec (x−y) -sec² (2-y)-z 當…

A: find derivative dxdy from equation xy=tanx-y

Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

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Q: Write the Taylor series for f(x) = xº about x = −4 as Σ Cn (x + 4)". n=0 Find the first five…

A: The given function is  f(x)=x3 about x=-4.

Q: of a rectangle.

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Q: Find the work done by the force field F(x, y, z) = (x - y², y - z², z - x²) on a particle that moves…

A: Work done on particles: W = F.dr

Q: r = 12 sin 18ti + 12 cos 18tj

A: Given :

Q: Solve y"+y' + y = 6sin (2x) supo

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

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Q: Find the average value of the function f(x) = 3x³ on the interval 2 ≤ x ≤ 6

A: The average value of a function is found by taking the integral of the function over the interval…

Q: the

A: We will solve the Differential equation.

Q: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

A: use the constrained variation to maximize the volume of an open cone when the surface area is 2π

Q: k1 (k+ 1)².4k ak+1 lim ||

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Q: Use Green's Theorem to evaluate the line integral ſ (y + e√x) dx + (2x + cos y²) dy, where the given…

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Q: 2. lim lim (x-i) tan (x 3 x) x>1 (x+1) sind (2x-2)

A: We have to find the limit of the given function without using l' hopital's rule.

Q: Let ƒ(x) = √x(2 − x)². Use the local linear approximation of f(x) at x 1 to estimate the value of…

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Q: 2. Find the area between the curve y=-x and y+x²= 2x.

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Q: Find the value k that makes the function continuous. kx 10, x 10 M > f(x) = _ 4x + 10, x < 10 Submit…

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Q: Evaluate the integral 13 ƒ(x)dx geometrically for ƒ (x) = { |3 − x ; x ≤ 5 2; x > 5

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Q: Prove the identity. sec²x+csc²x = sec²x csc ²x Note that each Statement must be based on a Rule…

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Q: . DO NOT SIMPLIFY YOUR ANSWERS. - 1. log₂ 19²( √/2x² + y) + tan(x² − x²) = sin^¹(x² − 1) + ² Find d

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: Here, the given series is: ∑n=1∞7n2(2n+1)! Let, an=7n2(2n+1)!; n≥1

Q: 32-37 FOURIER INTEGRALS AND TRANSFORMS Sketch the given function and represent it as indicated. If…

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Q: - y' + y = 2 sinx when y(0) = -1

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Use Newton's Method to approximate the zero(s) of the function. Contine Rx)-x+2.7x² +3.55x-2.422…

A: answer is in next step

Q: Find the exact length. T=0², 0≤0 ≤ 2π ° 4[G²+1²] ²3 [(x² + 1)² - 1] [(²+1)-1] ° 4[68² +1²]

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