lim ∞ + X 3x² + 2x - 1 3√7+4x+x² + 3x

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A: Given

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A: see below the answer

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A: Option (B) Diverges

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A: The difference quotient of a function f(x) is given by, f(x+h)-f(x)h

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A: Explained below

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A: Differentiation need to be done appropriately.

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A: By considering u=ax+b we can integrate it.

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A: We can find the length of arc by applying length of arc formula.

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A: Equating the two given points,

Q: polar of a point are giv the pon R/2 R/2 6f 4 4 2 2 -6 -2 4 6 -2 -4 R/2 R/2 6. 4 4 -6 -4 2 -6 -2…

A: Topic = Geometry

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A: We need to find horizontal asymptote and graph.

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Q: 4)3y-4z = -2 3x-4y+z=-9 3-3x-2y-2z = -5 %3D |

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A: This question is related to linear equations, we will solve it using given information.

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Q: dy (x– 2)³ · (2x + 1)ª Find if y = dx|, e2x . Vx+8 Use logarithmic differentiation.

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Q: 5. Use the shell method to find the volume of an ellipsoid formed when that part of the ellipse x2 +…

A: Given

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A: We have to find the sum of series.

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A: The given curves are; x=8+2y-y2, x=0 (y-axis), y=-1 and y=3   So, the bounded region is as shown…

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Q: 1. Get the first derivative f': 2. Find the factors: 3. Find the critical numbers: 4. Get the second…

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A: answer is in next step

Q: 1 dx x² +1 e +

A: solution:-∫02ex+1x2+1dx=∫02exdx+∫021x2+1dx=ex02+tan-1x02=e2-e0+tan-12-tan-10=e2-1+tan-12     Ans

Q: Use the Fundamental Theorem of Calculus to find the derivative of y = cost dt %3D [NOTE: Enter a…

A: Topic = Derivative

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A: Question- Identify the definite integral that computes the volume of the solid generated by…

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Q: 1. Find dy for each of the following: dx d) y = e +x° +e° e) y = x° Inx 1) In(x + y) = e*-

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Q: Identify the type of quadric surface defined by the equation 6x² + 3y² + 2z² = 36, and find all x-,…

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Q: के For the function f(t, x) = sin(4xt +9x), find and da Əf 4x6x(4xt+9α) (Type an exact answer in…

A: topic- partial differentiation

Q: s dx x√√√2x-x²

A: topic - indefinite integral

Q: 1. If f (x) = 5x – 6x2 + 4x - 2 find f'(x) and f'(2).

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Q: 4. Consider the line D: "2¹ = = = ²/² = = z2 and the plane P: 2x + 2y — z = −3. a) Find the points…

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Q: 1. Find the area bounded by: x=y² and y=-x².

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