x = t(t? – 147), y = 4(t² – 147) a.) Determine the point on the curve where the tangent is horizontal. b.) Determine the points t1, t, where the tangent is vertical and t < t, . 2 =

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Q: Find the points on the curve a = t – 16t + 1, y = t² + 12t – 8 that have: %3D A. a horizontal…

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Q: Find the plane tangent to the function, z=x(sqrt(y)) at (3, 49).

A: Given: The function is z=xy and the point is (3, 49).

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Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

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Q: Find the points on the curve a = ť² – 14t – 9, y =t² + 14t + 1 that have: | A. a horizontal tangent…

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Q: Find the length of the curve. r(t) = ( 8t, t², ), 0 <t< 1 %3D 12

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Q: Find the points on the curve æ = t² – 6t – 8, y = t² + 14t – 6 that have: A. a horizontal tangent…

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Q: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

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A: Given: u-(t)=(met2-t)2i-4mt+1j+t-mt2+1k at t=0 First we will find tangent line of the curve…

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A: Given function, fx,y=yx2+1 To sketch the curve of the function.

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Q: nd the tangent plane to the equation z = a? – 4y? – 2y at the point ( – 3, 3, – 33)

A: In this question, concept of tangent  is used. Tangent A tangent is the line that runs parallel to…

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: Find the points on the curve x = t – 16t - 3, y = t + 6t + 8 that have: %3D A. a horizontal tangent…

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Q: Q5. The curve y = ax? + bx + c passes through the point (1, 2) and is tangent to the line y =x at…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Find the points on the curve a = t? – 4t + 1, y = t² + 8t – 8 that have: A. a horizontal tangent…

A: Let's find.

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Find the points on the curve  x=t^2−18t−4, y=t^2+10t+6   that have: a) a horizontal tangent line,…

A: We have to solve by derivative rule

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Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

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Q: Find the points on the curve t2 – 14t – 1, y = t² + 6t + 5 that have: х — A. a horizontal tangent…

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Q: ind the points on the curve zx? + 4y? = 1 that have a horizontal tangent line.

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Q: F. dr where F = yzi + xzj +xyk and C is the curve x = t, y = 2t², z = –2t² with 0<t < 1.

A: Given F=yzi+xzj+xyk and r=ti+2t2j-2t2k Now the vector field along the curve can be given by…

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Q: Q4: Find the angle between the tangents to the curve R(t) = t²i+ 2tj – t³k at the points t = F1

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Q: x(t) = t² + 2t – 3 %3D y(t) = t² + 2t – 30 What is the length of the segment of the curve between t…

A: Given parametric curve is xt=t2+2t−3 and yt=t2+2t−30. We have to find the length of the segment of…

Q: Find the points on the curve C where the tangent is horizontal C: x = t + 6t, y = t' – 3t. O A.…

A: First we have to calculate dy/dt then,we have to find out the value of t for which dy/dt =0 To find…

Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Find the tangent plane to the equation z 5x? – 2y? – 5y at the point (3, 0, 45).

A: We need to find the tangent plane equation at (3,0,45)

Q: Use the formula z = ['(t) x r²(c)]. r²(c), Ir'(t) x r"(t)1² r(t) = 9t, to find the torsion of the…

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Q: Jy (a, b)? b.) Determine for what points g(x, y) = x – 2 In|x + y| is differentiable.

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Q: e, Find at the giren point on eauation Of the tangent live. to the corve. X=46",y=f'+|,(4,0)

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Q: consider a curve r(t) = 2t³ i+ 2t j+v6t² k calculate the length of the curve in the interval 0 st 3

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Q: Express the curve by an equation in a and y given #(t) = t² and y(t) = 2 t4 + 6. а) x = 4 y? + 5, y…

A: To convert the parametric equation into cartesian we must have to eliminate parameter t from both…

Q: Find the length of the curve. r(t) = 8 i + t2 j + t3 k,    0 ≤ t ≤ 1

A: Given:

Q: Find the equation of the tangent plane to the graph of f(x, y) = 8x² – 2xy? at the point (5, 4). A)…

A: We first find the partial derivatives  So the direction vector of the normal is = (48,-80)

Q: Find the length of the curve traced by r(t) = t^2 i + (((t^3)/3) + 2)j, for 0 ≤ t ≤ 1

A: The solution is given as

Q: Find the tangent plant to f(r, y) = x² + 3ry + 5y² at the point (1,2).

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Q: O tind dyldx and aby/ax?. Find the point on the curve where the tangent line is horizontal. X= t? y=…

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Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

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Q: Find the point at which the line 7(t) +t intersects the | xz plane.

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Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: Let the line y = mx + 2 be a tangent to the curve y = In-, at the point P. i) Find the coordinates…

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Q: Find the tangent plane to the equation z x? – 2y + 2y at the point (- 1, 5, – 39). z =

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Q: Let y(t) = (1/2)te*/2, 0<t< 2n What is the terminal point of the curve? — 2п

A: Terminal point of curve is obtained at terminal point of path.

Q: For (z +y)? = z² -f find the points where the tangents are horizontal.

A: