Solve the following differenti- d'y 3. +2y=e"; dx dx

Q: V4-x² c 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x²+y² A 128/15 в) 16/89 c) 23/6 6.

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: This question can be solved using the concept of volume of solid of revolution.

Q: 11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Current Attempt in Progress Find the area of the region inside the circle r = 18 sin 0 and outside…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: find the equation for x in y=3x-x^3

A: Solving

Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

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Q: Find the exact arc length of the curve over the stated interval. 1 1 +y2, from y = 1 to y = 4 x = 4°

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Q: Question 3 Express the area of the given surface as an iterated double integral, and then find the…

A: Let's find.

Q: 2. Determine whether the statement is True or False. If it is false, explain what makes it false, or…

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Q: n/2 sine Evaluate the iterated integrals r cos e dr de 0.

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Q: Find the area of the region enclosed by the curves y = x² and y integrating with respect to y. = 6x…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: f(x)= 2cos (x) − 6sec (x)+3 =

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Q: y=x*(1-x)ª 4-4x 4+4x

A: Use the chain rule of differentiation.

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: Evaluate the definite integral. 14t i + e*j+t k)dt (el4 – 1) i – (e-1 – 1) j + k 1-(6" -1) + i- (e~-…

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt dt the product directly…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, g) = |(?, ?) y = 1

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Q: Find the area of the region using a double integral. The region bounded by y = 4x°, 2x + y = 6, and…

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Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

Q: Find the inverse of the function. f(x) = 9-2x^3 f^-1(x) =

A: THIS QUESTION CAN BE SOLVED USING THE CONCEPT OF INVERSE OF FUNCTION.

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = T, using 4 trapezoids.…

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Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Find the area of the region inside the circle r = 24 sin 0 and outside the cardioid r = 8 + 8 sin 0.…

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Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. e…

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

A: Given

Q: 4 mm/s when these three sides are 5cm, 4 cm sides x, y and z increase at 6 mm/s, 5 mm/s and Fig.…

A: we have to find rate of change of AC.

Q: Find the divergence of F(x, y, z) =(a -1 Y, y? + 1' 3xz2 + 2y ) at (2,0, – x COS

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Q: Find the surface area of that portion of the surface Z = 4 -x that lies above the rectangle R in the…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 7 cos(t)i…

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Q: Find the area of the region inside the circle r = 18sinθ and outside the cardioid r = 6 + 6 sinθ.

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Q: Find the exact arc length of the curve over the stated interval. 1 1 Gy, from y =1 to y = 3 12 NOTE:…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: We need to evaluate integral using Green's theorem.

Q: Consider the parallelepiped with adjacent edges u = 4i + 6j + k v = i +j+ 9k w = i + 7j + 6k Find…

A: Given; u=4i+6j+k , v=i+j+9k , w=i+7j+6k Volume (V)=?

Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

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Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Find the area of the region enclosed by the rose r = 18 cos 30. NOTE: Enter the exact answer. A = T

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 19, (1,…

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

A: Given

Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(7,…

A: To find the directional derivative of the function at P in the direction of v.hx, y, z=xyz, P7, 2,…

Q: Evaluate the iterated integral. 1 z y SS§ 9ze=v² dr dy dz

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Q: Find the area of the region bounded by the graphs of f (x) = x³ and g (x) = x. (A) 1 c) 0.5 3.

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

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Q: loge (cos x) e. lim x V1+x2 -1

A: e.limx→0logecosx1+x2-1