Suppose r(t) = i+t²j+2tk. Find the length of the portion of this curve that goes from the point G, 1,2) to (9,9,6). Also, give an expression for the curvature as a function of t.

Q: Find the length of the following curve. y = 2x + 4 on 3-2, 24 (Use calculus.)

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Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

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Q: Find values of a and c such that the tangent to y = ax2 + 12x + c is horizontal at the point (2,5)

A: Tangent is horizontal where derivative is zero

Q: Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Since we have to find value of a,b,c and d

Q: Consider the equation 2.61x² + y² = 1 +0.71x²y². In this question you will calculate the curvature,…

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Q: Find the distance between the pointx1 =−1, y1 =1, z1 =3 and the point x2 =1, y2 =1, z2 =1.

A: The first point is (-1,1,3) and the second point is (1,1,1) We will use the distance formula:

Q: What about the part where it has to be part of the curve r= sqrt(2cos(2theta))?

A: As per the question to evaluate the volume of a cylinder with specific geometric properties, we can…

Q: 2. Find an equation for the tangent line to the cycloid x = et + 3, y = t² et - 3et + 2 at the point…

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Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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