Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

Q: The slope of the tangent line to the curve x = t cost and y = t sin t at the point corresponding to…

A: The slope of tangent line

Q: Find the equation of the tangent plane to z=e^y+x+x^5+10   at the point (3,0,257)

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Q: Given the xーxy+y? %3D 9 2. Curve 6. Find the coordinates of the POTnts on the Curve where the…

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Q: Find equations for the horizontal and vertical A)y= at (1, 똥) B) z = 0 at (0, ) D) y = 2 at (2, *)…

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Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

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Q: Consider the parametric curve x = Vt , y= 3t –1, for t20. Find the slope of the tangent line to this…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the equation of the tangent plane to z = ey + x + x2 + 11 at the point (5, 0, 42).

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Q: Find an equation of the tangent plane to R(u, v) = (e" sin u , eº cos u , e¯-" ) at the point where…

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Q: Find the equation of the tangent plane to z=e^y+x+x^2+10 at the point (2,0,17).

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Find the points on (t + sin t, t − 2 sin t) where the tangent is vertical or horizontal

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Q: Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y =…

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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.

Q: Find the interval on which the curve dt 3 +t + 212 y = is concave upward.

A: Given: y=∫1x13+t+2t2dt

Q: Show that the tangent at P(x,,y,) on the curve -1 Vx+Jy=Ja is yy, ,=a

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Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

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Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

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Q: Find the equation of the tangent plane to z=e^x+y+y^2+ 9 at the point (0,4,30)

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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: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: Find the unit tangent vector to the curve defined by 7 r(t) = (5 cos(t), 5 sin(t), 2 sin² (t)) at t…

A: To find the unit tangent vector to the curve defined by r→t=5 cost, 5 sint, 2 sin2t

Q: compute the length of the curve over the given interval.  r(t) = (cost,sin t,t3/2), 0 ≤ t ≤ 2π

A: Derivative of a function is represented as the change in variable with respect to change in another…

Q: Find the vector equation of the tangent line to F(e) = 2 (e1-t) in t i + tan"1tj+ k at cos(t ) the…

A: To determine the vector equation of the tangent line.

Q: The parametric form of the tangent line to the image of f(t) = (4t², § , t – 2) at t = 3 is L(t) = |…

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈t2, t4〉, t = −2

A: We have given equation of curve rt=t2,t4 a point on this line  r1=-22,-24=4,16 A vector parallel to…

Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: Find an equation for the tangent plane of z 3.xy? + y + 2 at the point (-1, 1, 0).

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

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Q: Find the equation of the tangent plane to z = ey + x + x² + 7 at the point (5, 0, 38). = Z |

A: To find the equation of tangent plane to z=ey+x+x2+7  at the point 5,0,38In general the equation of…

Q: At the point (a, b) the curve T =t-4t, y=t2 +2t, t eR has a vertical tangent line. What is the sum a…

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Q: Find the equation of the tangent plane to z = e9 +x + x³ + 6 at the point (3, 0, 253).

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Q: Find the vector equation of the tangent line to F(t) = 2 (e-) in t i+ tan-tj+ the point where t = 1.…

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Q: Find the unit tangent vector to the curve defined by r(t) = /16 – t² ) at t = (- 4t, – 3t, T(- 2) =

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Q: The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

A: To find the parametric form of the tangent line to the image of f(t)

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

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Q: Find an equation of the tangent line to the curve a = t sin t, y = t cos t att = 5. Lütfen birini…

A: Given,  x= t sin(t)y=t cos(t) To find : The equation of a tangent line. Solution: The slope of…

Q: The parametric form of the tangent line to the image of f(t)=⟨4t2,5t,t−2⟩ at t=3 is L(t)=

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Q: Find the points on the curve x = t – 16t + 4, y = t + 16t + 5 that have: A. a horizontal tangent…

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Q: Find all points (x,y) on the curve C:x(t) = t² + 6t + 12, y(t) = 5t – 8 where the tangent line to…

A: We need to find the point (x,y) on the curve C,whose tangent line to the curve is vertical

Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: Find the points on the curve x = t2 14t + 1, y = t + 12t +1 that have: A. a horizontal tangent line…

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Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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Q: Find the equation of the tangent plane to f(x,y)=√2xy+ 1 at the point            (2, 2),and use it…

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Q: The parametric form of the tangent line to the image of f(t) = (5t², 2,t – 2) at t = -1 is L(t) =

A: Topic = Application of derivative

Q: s Find the exact slope of the tangent line to the parametric curve π t = x = 9 cos(t) y = 4 sin(t)…

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