14.4 Exercises1-6 Find an equation of the tangent plane to the given surface atthe specified point.1. z = 3y² – 2x² + x, (2, –1, –3)2. z = 3(x – 1)² + 2(y + 3)² + 7, (2, –2, 12)%3D3. z - Vxy, (1, 1, 1)4. z = xe", (2, 0, 2)5. z = x sin(x + y), (-1, 1,0)6. z = In(x – 2y), (3, 1, 0)

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Answered: 1-6 Find an equation of the tangent…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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In Exercises 1–5, find equations for the (a) tangent plane and (b) normal line at the point P0 on the given surface. 1. x2 + y2 + z2 = 3, P0(1, 1, 1) 2. x2 + y2 - z2 = 18, P0(3, 5, -4) 3. 2z - x2 = 0, P0(2, 0, 2) 4. x2 + 2xy - y2 + z2 = 7, P0(1, -1, 3) 5. cos paix - x2y + exz + yz = 4, P0(0, 1, 2)
In Exercises 1–5, find equations for the (a) tangent plane and (b) normal line at the point P0 on the given surface. 1. x2 - xy - y2 - z = 0, P0(1, 1, -1) 2. x + y + z = 1, P0(0, 1, 0) 3. x2 + y2 - 2xy - x + 3y - z = -4, P0(2, -3, 18) 4. x ln y + y ln z = x, P0(2, 1, e) 5. yex - zey2 = z, P0(0, 0,1)
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1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) = x2 + e9y ln(x-y). ○ Compute ∇f at the point (1,0). ○ Compute the derivative of f(x,y) at the point (1,0) in the direction (3,-4). ○ Explain the geometric relationship between the answer found in part (a) and the surface defined above.
Suppose that z is an implicit function of x and y in a neighborhood of the point P = (1, 1, 0) of the surface S of the equation: xy + yz + zx = 1 An equation for the line tangent to the surface S at the point P, in the direction of the vector w = (1, −2), corresponds to: The answers are in the attached image.
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1-6 Find an equation of the tangent plane to the given surface at the specified point. 1. z = 3y² – 2x² + x, (2, –1, –3) 2. z= 3(x – 1)² + 2(y + 3)² + 7, (2, –2, 12)