Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0). Determine if this line intersects the ellipsoid x2 +16y2 +z2= 16. If so, identify the point(s)

Q: Find an equation for the plane that is tangent to the surface z=ln(x2+y) at the point P(0,1,0).

A: we have to find the equation of the tangent plane

Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

A:

Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

A:

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 - 2xy + y2,  (2, 3,…

A:

Q: Find an equation of the tangent plane to the surface S : za? – xy – yz = 18 at the point (0, –2, 3).…

A: We know that an equation of the tangent plane to the surface Fx, y, z at the point x0, y0, z0 is…

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 2 at the given point (1, 3, 12)

A: Given surface, So

Q: Find an equation for the tangent plane to the surface z = 4xy® + sin(rx) at the point (1, 1, 4)

A:

Q: 4. Find the equation of the tangent plane to the surface Z = = 5tan(x) – sin(3y) at the point (xoyo)…

A:

Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

A:

Q: Starting from the point (3, 1, –1), reparametrize the curve x(t) = (3 + t, 1 – 2t, –1 – 2t) in terms…

A: We need to reparametrize the given curve in terms of arclength. The solution is given below.

Q: Find an equation of the tangent plane to the surface z=8/2x+4y at the point (2,1,1). z=

A: Please see the explanation below

Q: 1. Give an equation of the tangent plane to the surface z = In(4y – x) at the point (3,1,0). 2. Use…

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

Q: 6. Find an equation of the tangent plane to the surface z = y² – x² at the point (-4, 5, 9).

A: Recall: Equation of the tangent plane to the surface z=f(x,y)  at (x0,y0,z0) is        fxx-x0 +…

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

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

A:

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

A:

Q: Find an equation of the tangent plane to the surface z=−1x2+3y2−3x+1y+1 at the point (2, 2, 5).

A:

Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = ln (x2 +…

A: Given z=ln(x2+y2)

Q: 3. Find an equation of the tangent plane to the paraboloid defined by z= 5x +4y? at the point…

A: The given equation is; z=5x2+4y2 at the point (-1,1,9).

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = In(x - 3y),…

A: Here, the surface is: z=ln(x-3y) To find the equation of the tangent plane at the point (7,2,0).…

Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

A:

Q: Find an equation of the tangent plane to the surface at the given point. 6. f(x,y) = x² – 2xy + y²,…

A: fx, y=x2-2xy+y2,    1, 2, 1. Partially differentiating with respect to x, we get fxx,…

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

A:

Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

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

A:

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

A:

Q: Find the tangent plane to the graph of **yz +z'e* -y² = 5 at (1,3,2).

A:

Q: Find an equation for the tangent plane to the graph of z = xe' cos z – 2 - at the point (2,0,0). 1.…

A:

Q: 4. Find an equation for the tangent plane to the surface z = 3x + 5y + arctan in the point (0, 1,…

A:

Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: x² = y + 3y.

A:

Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

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

A:

Q: 1. Find the equation of the tangent plane to the surface cosh [exp (x²y)] = Z y? at the point where…

A: We will find out the required equation of tangent plane.

Q: Find an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)

A:

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: Find the maximum, minimum and inflection points of the fur y= 3 sin 2x at [0, T].

A: Solution:-

Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: 3. Find an equation of the tangent plane to the surface z = 2xy + 4y xy-2x at the point (1,1,-6)

A:

Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

A:

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2,…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

Q: Find the equation of the tangent plane to the surface z = 3 e^(x−y) at the point (4, 4, 3)

A: We find the equation of the tangent plane to the surface z = 3ex-y at the point (4, 4, 3).

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

A: