Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Videos
Question
Chapter 16.6, Problem 3PT
To determine
To choose: The appropriate option for the statement “The equation of the tangent plane corresponding to
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find an equation of the tangent plane to the surface
x² + 2y² + z² = 175
at the point (5, -5, 10).
O 5 (-5)-10 (y + 5) +20 (z
O 10 (x - 5) - 20 (y + 5) 20 (z
O 10 (x - 5) + 20 (y + 5) +20 (z - 10)
10) = 0
| |
10) = 0
m
O 10 (x - 5) - 20 (y + 5) + 10 (z - 10) 10
O 10 (x - 5) - 20 (y + 5) +20 (z 10) = 0
-
5. a) Find parametric equations for the tangent line to the curve of intersection between the paraboloid z = x²+y² and the ellipsoid 4x² +y²+z² = 9
at the point (-1,1,2). Also, find a vector function that represents the curve of intersection.
b) Find parametric equations for the line tangent to the curve of intersection between S₁: x² + y² = 4 and S₂ : x² + y² - z = 0 at the point
(√2, √2,4). Find a vector function for the curve of intersection.
It can be shown that the parametric equations
x = x1 + (x2 – x1)t, y = y1 + (y2 – yı)t,
where 0
Chapter 16 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 16.1 - For F(x,y)=(x+y)i+(2x4y)j, which vector, a, b, c,...Ch. 16.1 - Prob. 2PTCh. 16.1 - Prob. 3PTCh. 16.1 - True or False: F(x,y)=2yi+2xj is conservative.Ch. 16.2 - A definite integral for C(x+y)ds, where C is the...Ch. 16.2 - True or False: The curve at the right appears to...Ch. 16.2 - A definite integral for CFdr, where F(x,y)=x2i+y2j...Ch. 16.2 - Prob. 4PTCh. 16.2 - Prob. 5PTCh. 16.3 - Prob. 1PT
Ch. 16.3 - Which curve is simple but not closed?Ch. 16.3 - Prob. 3PTCh. 16.3 - Prob. 4PTCh. 16.3 - Prob. 5PTCh. 16.4 - Prob. 1PTCh. 16.4 - Prob. 2PTCh. 16.4 - Prob. 3PTCh. 16.4 - Prob. 4PTCh. 16.5 - Prob. 1PTCh. 16.5 - Prob. 2PTCh. 16.5 - Prob. 3PTCh. 16.5 - True or False: div curl F = 0.Ch. 16.5 - Prob. 5PTCh. 16.5 - Prob. 6PTCh. 16.6 - Prob. 1PTCh. 16.6 - Prob. 2PTCh. 16.6 - Prob. 3PTCh. 16.6 - Prob. 4PTCh. 16.6 - Write an iterated integral for the area of that...Ch. 16.7 - Prob. 1PTCh. 16.7 - Prob. 2PTCh. 16.7 - Prob. 3PTCh. 16.8 - Prob. 1PTCh. 16.8 - Prob. 2PTCh. 16.8 - Let F(x, y, z) = zi + xj yk and the curve C be...Ch. 16.9 - Prob. 1PTCh. 16.9 - Prob. 2PT
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Similar questions
- 2) Find an equation for the plane tangent to the surface z = √√√x² + 5y at the point (6,-4,4)arrow_forwardFind an equation of the tangent plane (in the variables x, y and z) to the parametric surface.r(u,v)=⟨4u,4u^2+5v,−3v^2⟩ at the point (4,-6,−12).arrow_forwardFind the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).arrow_forward
- Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y² and the surface x = e". Write the equation so that one of the functions is simply t. x(t) = y(t) = = z(t): =arrow_forwardFind an equation of the tangent plane to the surface g(x, y) = x² - y² at the point (7,2, 45). -y O 14(x-7)+2(v-2)(z-45) = 0 O 14(x-7)+4(y-2) + (z-45) = 0 14(x-7)-4(y-2)-(z-45) = 0 O 7(x-7)-2(y-2)-(2-45)=0 O 14(x-7)-4(v-2) + (z-45) = 0arrow_forwardFind the (linear) equation of the tangent plane to the surface z = 5y² - 3x² + x at the point (2,-1,-5). Your answer should be in the form of an equation, e.g., something like ax +by+cz = d or a(x − xo) + b(y − yo) + c(zzo) = 0 would work. Equation:arrow_forward
- Find a plane through the point (2,-3,7) and orthogonal to the line 3x - 3y -z = ·22 QUACLI x(t) = 4 + 3t y(t) = 2 - 3t z(t) = X -8-tarrow_forwardA parametric representation of the curve of intersection of the two surfaces x2 + 5y2 - z = 0 and z - 4y2 = 36 is given by the vector equation : r (t) = 6cosh(t) i + 2sinh(t) j + (36 - 16 sin²(t) ) K ,0sts 2n r (t) = 6cos(t) i + 2sin(t) j + (36 - 16 sin2(t) ) k , 0 st s 2n = cos(t) i + sin(t) j' + (36 - 16 sin²(t) ) k ,0 st s 2n %3D r (t) = 6cos(t) i + 6sin(t) j + 36(1 + 4 sin2(t) ) k ,O st s 2n r (t) = cos(t) i + 3sin(t) j + 36cos2(t) k ,0 st s 2Aarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Introduction to Triple Integrals; Author: Mathispower4u;https://www.youtube.com/watch?v=CPR0ZD0IYVE;License: Standard YouTube License, CC-BY