Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos (0 + 14) (Use symbolic notation and fractions where needed.) dy %3D d0

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A: 13)f(x)=x34-4x14f'(x)=34 x-14 -414 x-34f'(x)=34 x-14 -x-34 f'(x)=034 x-14 -x-34 =03 x-14 =4x-34 34…

Q: 6 6 iwen ["r*dz = 320, x³ dx x dx 16, dx = 4, evaluate the following using properties of definite…

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Q: FOTE: Enter the exact answer. dx dy = VT

A: A detailed solution is given below.

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A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

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Q: Evaluate the double integral f(r, 0) dA. -7 cos(0) r dr de 497 2 Sketch the region R. 7/2 A/2 6 2 4…

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Q: 4. Show that a b a +

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

Q: V4-y? cv8-x²-y² Use cylindrical or spherical coordinates to evaluate the integral. JoJ Vx?+y? A 32…

A: To find the value of the given integral.

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Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

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Q: 0, 1, 2, 3, and 4 about x = xo Find the Taylor polynomials of orders n = and then find the nth…

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Q: Find the exact arc length of the curve over the stated interval. y = 8x2/3, from x = 1 to x = 8…

A: The expression for the arc length of the curve is: L=∫x1x21+dydx2dx   Given; y=8x23x1=1 &amp; x2=8

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Q: 3. dy Find if y 2xy - x: dx = cos X using implicit differentiat

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Q: Find curl (9z i + 10x j + 5y k). curl (9z i + 10x j + 5y k) = ( i )i + ( i j + ( i

A: Curl

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A: Use derivative concept

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Q: 2.1 Find the value of x and y from the given complex equation (-2 + i)x + 2y =1+ 3i. 2.2 Write the…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -72

A: To evaluate: ∫02∫-72y2∫-48zyz dx dz dy

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: Find the curvature and the radius of curvature at the point t = 0. %3D x = e' cos(t), y = e' sin(t),…

A: r(t)=et cos(t) i+et sin(t) j+7et kr'(t)=[etcost-etsin(t)] i          +[etsint+etcos(t)] j +7et k…

Q: ... 3x+ 2y + 4z = 12 12 15

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Q: Consider the curve (y2 = 9 +x) that defines y as an implicit function of x. If P (xo, yo) is the…

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Q: Find the area of the region inside the circle r = 12sinθ and outside the cardioid r = 4 + 4 sinθ.

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Q: 20 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer.…

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