ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

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

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Q: (b) Find a , b and c if the curvey = x + a x + b and y =c x + x have tangent lines paralle to each…

A:

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: The tangent line to the graph of y = In(2x) is perpendicular to z + 4y = 1 at the point where Select…

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: r(u, v)=(w+v)i(u-v)j+v²k at the point P(2, 0, 1)

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Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

A:

Q: Which of the following is the equation of the tangent plane to the surface z = 3x2 +x-y²+y at the…

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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: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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

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Q: Show that if P lies on the intersection of the two curves x2 - y2 = c and xy = d (c, d constants),…

A: Given : The two curves x2 - y2 = c and xy = d intersect at point P where c and d are constants.…

Q: Find the distance between the point (-2m, 0, -m) and the tangent line of the curve ū(t)= (me* – }i--…

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

Q: Consider the curve C parametrized byx = (t^2+1)/(t^2-1) and y = (2t)/(t^2-1) for all t in (−∞, −1 )…

A: Given:

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

A:

Q: Let f(x, y) = 2xy – 4x² + 3y². %3D Then a standard equation for the tangent plane to the graph of f…

A: The function is given. Find the partial derivative fx and fy at the given point. Given,…

Q: find a parametrization c(t) of the curve satisfying the given condition. y = 3x − 4, c(0) = (2, 2)

A: It is given that,

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈1 − t^2, 5t, 2t^3〉, t = 2

A: r(t) =(1-t2, 5t, 2t3) at t=2

Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

A:

Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

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Q: Find the equation of the tangent plane to z = e® +y+y +1 at the point (0, 2, 12). 2 =

A:

Q: Use Green's Theorem to evaluate | F. dř, where F = (Va + 4y, 2x + 9) C consists of the arc of the…

A:

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 a parametrization c(t) of the curve satisfying the given condition.  y = 3x − 4, c(3) = (2, 2)

A: To find the parametrization

Q: Find the point on the graph of z = 3x2 – 2y? at which vector n = (-12, –16, –2) is normal to the…

A: Shown below

Q: Find the unit tangent vector and the parametric equation of the line tangent to the given curve at…

A:

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: If the equation of the tangent plane to x2+y2-11z2=0 at (1,1, /2/11) is x+ay+Bz+y=0, then a+B+y=D

A: Given query is to find the equation of the tangent to the plane.

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

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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 unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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Q: Find the equation of the tangent line to the space curve r(t) = 2cos (t)i + 2 sin(t)j + tk at the…

A: The curve is given by: r(t)=2cos(t)i+2sin(t)j+tk

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: x² = y + 3y.

A:

Q: Find the tangent plane to the equation z = 3x2 + 4y? – y at the point (3,5,68)

A: We have to find the tangent plane equation to the given surface at a given point.

Q: Find a parametrization of the tangent line to r(t) = (ln(t))i + t^-5j + 5tk at the point t = 1

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Q: Find the equation of the tangent plane to z = e? + y + y² + 10 at the point (0, 5, 41). z =

A: Find equation of tangent plane from the given data

Q: Show that the vector-valued function r(t) = ti + 2t cos tj + 2t sin tk lies on the cone 4x2 = y2 +…

A: Given: Vector-valued function: r(t)=ti^+2tcostj^+2tsintk^ Cone: 4x2=y2+z2

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

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Q: Find an equation of the plane tangent to the following surface at the given point. z = tan (xy);…

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Q: Find the tangent plane to the function f(x, y) = sin(xy?) at (a,. Is it parallel to the plane 2x- 3y…

A: fx, y=sinxy2 Partially differentiating with respect to x, we get fxx,…

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

A:

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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Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

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Q: Find the diffrential equation of for each of the curves determined by the condition that at each…

A: length of subtangent =ydydx

Q: Find the tangent plane to f(1, y) = ar² + 5y² + 71²y² +9x +5y at the point (3, 6). %3D

A:

Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: 3. Find the equation of the plane tangent to the graph of f (x, y) = 3x + 4y – xy at the point (1,…

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