Q4: Find the unit tangent and unit normal vector at t = 2 on the curve x = t? – 1, y = 4t – 3, z = 2t2 – 6t where t is any variable. |

Q: Q2. What is the curl of the following vector function? v =x

A: Curl of a vector function is ∇ x v

Q: Ifr(t) = (sin t , cos t, 29- t), then determine a vector that is perpendicular to both unit tangent…

A: Given: r(t) = sin t, cos t, 29-t To determine: A vector that is perpendicular to both unit tangent…

Q: For the equation x² +2.xy – 3y =0, find the equation of the normal to the tangent line at the point…

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Q: Derivatives of vector-valued functions Differentiate the following function.

A: We have given the function;

Q: H.W. Find the unit normal vector to the curve at t=2, r(t) = 4t i-3 t j.

A: Unit normal vector is N(t)=T'(t)‖T'(t)‖ here T(t) is unit tangent vector and T(t)=r'(t)‖r'(t)‖ So we…

Q: Which of the following lines is perpendicular to the tangent line of y= х-3 at the point (2, –2) ? y…

A: We have to solve

Q: i If (a,ß), a<0 is the unit vector that is parallel to the tangent line to the curve y=-1x²-x at the…

A: The equation of the given curve is            y = -x2 - x        =&gt; dy/dx = -2x - 1 So, slope of…

Q: Q2) consider a particle moving in a curve defined by F(t) =sin 21, cos 21, 1. Find a. The velocity…

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Q: ü=i- where Use directional derivative definition to find Df (2.1) for the unit vector f(x y) = xy +1

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Q: b) Find Unit vector tangent and normal to the y=x² at P(²₂4) curne

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Q: Find the derivative in the direction f (x,y) - 11 - 8x²-64² 2 2 of the function The directional dori…

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Q: Find all values of x for which the tangent line of f(x) = A B С D -9 0,-9 -9,9 0,9 x²+18x+96 is…

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Q: On a metal plate in the shape of a rectangle, the temperature at a point (x,y) is given by; 100 3x²…

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Q: Find the point on the graph of z = - (2x² + y²) at which vector n = P = (-12, -10, -1) is normal to…

A: To find the point P on the graph of z=-2x2+y2 at which vector n=-12, -10, -1 is normal to the…

Q: Find an expression for dy in terms dz x² + y? + 8x 14y = 33 Using the dy found above find tho

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Q: Find the of rit)= <4cos(26), 5 sinlde), 3 css (AE when Unit Normal Vector

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Q: Find unit vector tangent and normals to the are y=1/2 X3+1/2. Point(1,1)

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Q: mZB А 60° C

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Q: The vector n = (7, –4, 2) is normal to the tangent plane to z = h(x, y) at (4, –5,6). Estimate…

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Q: If (a,B), a<o is the unit vector that is parallel to the tangent line to the curve y=3x2-x at the…

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