Find the equation of tangent plane, normal plane and rectifying plane to the curve of the position vector r(t) = (t²) i + (3t) j + (21) k at t = 2.

Q: 4. For the function f(x,y) = 2x² – 3xy + 8y? + 2x – 4y + 4, find a tangent vector to the level curve…

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Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 3x + 6y at the point…

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Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and…

A: Given the curve y=10+4x-x2 at (x,y)=(3,13).

Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

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Q: Find the directional derivative of the function f(x, y) = 1+5x/ỹ at the point (5, 1) in the…

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Q: Find the equation of tangent plane, normal plane and rectifying plane to the curve of the position…

A: The position vector rt=13t3i+3tj+12t2k at t=-1. Then we have to find the tangent plane and normal…

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: For the curve x = cos t , y = sin t , z = t, find a. an equation of the tangent line at the point…

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Q: Find the directional derivative of the function at the point in the direction of the unit vector. 3…

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Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

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Q: Find the directional derivative of the function f(r, y) = 1+5x /j at the point (5, 1) %3D in the…

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Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

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Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: /Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A: Given eq. of surface z=9-x2+y2 at the point 1,2,4             (1)

Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)

A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…

Q: Find the equation of the plane tangent to the graph of z + xyz = 33 at (1,2,3).

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Q: Compute the equation of the plane tangent to the surface x^2+3 y^2+z^3 = 8 at the point (2,1,1).

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Applications of derivatives

Q: Find the directional derivative of the function f(, y) = In(x +y°) at the point (- 1,3) in the…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the directional derivative of function f(x y)=x°e' at the point (1,1) and direction of vector…

A: Given:       fx,y=x2ey    at the point 1,1 and direction of vector v=2i      fxx,y=∂∂xx2ey…

Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

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Q: Find the tangent plane of the function f(x, y) = √2x² + 2y² at (1,1). Is it parallel to 2- the plane…

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Q: The directional derivative of xy f(x, y) = x + y) at (1, 1) in the direction of the unit vector at…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A: The above problem is solved.

Q: Find the equation of the tangent plane to z=e^y+x+x^2+1 at the point (5,0,32). z=?

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Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

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Q: Find the directional derivative of the function f(x, y) = 1+5x/ at the point (5, 1) in the direction…

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Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

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Q: Find an equation of the tangent plane to the surface z = 24 3z+4y at the point (4,3, 1).

A: Use equation of tangent plane

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

A: Equation of tangent plane on the surface z=f(x,y)  at the point (a,b,c)  is given…

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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Q: Find the derivative of f(x, y) = e*y + eY at the point (1,3) in the direction of the vector

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Q: The directional derivative of xy f(x, y) = V2 (x + y) at (1, 1) in the direction of the unit vector…

A: We have ,  f(x , y) = xy2x + y   We know that , directional derivative at any point x , y is defined…

Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).

A: This question is related to 3D geometry and equations of plane and lines,  we will solve it using…

Q: Find the directional derivative of the function f(x, y) = ln(x³ + y*) at the point (2, 1) in the…

A: we will find the directional derivative

Q: Find the directional derivative of the function f(x, y) = x²y° in the direction of the vector at…

A: Concept:

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Find the equation of the tangent plane to the surface y = 2x² – z² at the point (0,-1, 1)

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Q: Find an equation of the tangent plane to the surface z = √(9 − x2 − y2), at the given point (1, 2,…

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with…

Q: Find the directional derivative of the function f(x, y) = In(x² + y*) at the point (– 3, – 1) in the…

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Q: Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2)…

A: Given equation: x2+y2+z2=9 Consider the given equation, fx,y,z=x2+y2+z2-9=0

Q: Find the directional derivative of the function f(x, y) = In(x + y?) at the point (– 1, – 2) in the…

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Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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