Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (4, 0, 0)

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: 1. Find an equation for the tangent plane to the surface x cos z + yře*z =4 at Po(3, –1, 0)

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Q: Write the equation of the tangent line in Cartesian coordinates for the given parameter t. x = et, y…

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Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x? + 3y2 , x…

A: Topic- application of derivatives in 3-D

Q: 11. Find an equation of the tangent plane to the surface Va+Vy+Vz=4 at the point P(4,1, 1). 12. Find…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Given a surface f(x,y) = -3x + (-1)y. Find the derivative in the direction of v = at the point (2,…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y? + z? = 14, (1,…

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Q: The parametric form of the tangent line to the image of f(t) = (4t2, ,t+ 4) at t = 1is L(t) =

A: First we will find the tangent vector by differentiating f

Q: Find an equation of the tangent plane to the graph of F(r, s) at t F(r. s). - (3r4 1 + 1), (-1, 1.…

A: Introduction: Let z=f(x,y) denote the equation of a surface S in R3, and P=(a,b,c) denotes a point…

Q: (aj.G) x - 3x 4 3, find G'(a) and use it to find equations of the tangent fines to the curve y=x…

A: Given that       G(x) = x2 -3x+3  Here we have to find G'(a) and by using it find the equations of…

Q: nd an equation for the tangent plane to the surface z = f(x,y) = x² + 3xy – y° at the point (5, 1).

A: To find the equation of the tangent plane

Q: Given a surface f(x,y) = -3x + (4)y². Find the derivative in the direction of v = at the point (6,…

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Q: x2 + 4 Find the equation of the tangent plane to the surface z= 2 at (4,3,-3) | 9

A: The equation of the tangent plane to the surface at (4,3,-3) is, 6x + 2y + 3z = 7  The detailed…

Q: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x e' cos z at…

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Q: Find an equation of the plane tangent to the following surface at the given point. yz e xZ + 14 = 0;…

A: yzexz+14=0 f=yzexz+14 take partial derivative w.r.t. x fx=∂∂xyzexz+14 fx=∂ ∂ xyzexz+∂ ∂ x14…

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: (c) Find the equation of the tangent plane to S at the location where x = a and y = 0 (d) If S is…

A: The equation of plane is  ( r - a)n=0

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Find an equation of the plane tangent to the following surface at the given point yz e x2 - 6 = 0;…

A: Suppose we have equation of surface is then equation of tangent plane at point   is  .

Q: Find the equation of the plane tangent to the

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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 an equation of the plane tangent to the following surface at the given point. 13 cos (xyz) =- 2…

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Q: u(x, y) = arctan a = (-1,0)

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Q: Find the equation of the curve at any point  P(x,y) of a curve the subtangent equals -1/x

A: Given that the subtangent equals -1x. Then we get, tan θ2=-1x⇒tan θ=2 tan θ21-tan2 θ2⇒tan…

Q: Find an equation of the plane tangent to the following surface at the given point. XZ yz e +6 = 0;…

A: For the solution of the problem follow the next step.

Q: x² = y + 3y.

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Q: The Tschirnhausen cubic is the curve given by the equation x2 = y3 + 3y?. At which point(s) (x, y)…

A: Given query is to find the point of horizontal tangent.

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

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = (1, 4, 4) 10 Z 10…

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

A: Given,  x = t cost  y = t sint    We have to find the equation of the tangent at the point t = π.

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

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Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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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: Q4] Find the equation of the tangent plane and normal line to the surface z + 8 = x ey cos z at…

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Q: 4. For the function z = e cos(y) find the equation of a. The tangent plane to the given surface at…

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Q: at (2,-1,12). Find an equation for the tangent plane to the surface z=x -2xy +4y²

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

A: The given surface is: f(x,y)=x2-2xy+y2Given point is:  P=(1, 2, 1)

Q: Find the tangent plane to the equation z x? – 2y + 2y at the point (- 1, 5, – 39). z =

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Q: Assuming that z is a function of x and y, find the equation of the tangent plane and the equations…

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Q: Find equation of (a) the tangent plane to the given surface at the specified point. y = e^x cos (z)…

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Q: The parametric form of the tangent line to the image of f(t) = (2t², 3, t - 1) at t = 4 is t L(t) =

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Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: Find an equation of the plane tangent to the following surface at the given point. yz e x² + +42=0;…

A: The given equation is;  yzexz+42=0; (0,-7,6).

Q: Write the equation of the tangent line in Cartesian coordinates for the given parameter t. x = eVE y…

A: at t=1 x=e1=e1=ey=1-ln(12)=1-ln(1)=1-0=1 tangent point (x1,y1)=(e,1)equation of tangent line…

Q: E Find the tangent plane and the normal line to the surface x2 + y? - z2 = 18 at (3, 5, -4). %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.