Rog_Sec_14_4

Rog_Sec_14_4 - Math 20C Lecture Examples Section 14.4 Linear approximations and tangent planes A function z = f(x y of two variables is linear if

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
(8/17/10) Math 20C. Lecture Examples. Section 14.4. Linear approximations and tangent planes A function z = f ( x,y ) of two variables is linear if its graph in xyz -space is a plane. Equations of planes were found in Section 12.5 by using their normal vectors. Here we will need instead equations given in the next theorem for planes in terms of the slopes of their cross sections in the x - and y -directions. Theorem 1(a) (The slope-intercept equation of a plane) Suppose that the z -intercept of a plane is b , the slope of its vertical cross sections in the positive x -direction is m 1 , and the slope of its vertical cross sections in the positive y -direction is m 2 (Figure 1). Then the plane has the equation z = m 1 x + m 2 y + b. (1) (b) (The point-slope equation of a plane) Suppose that a plane contains the point ( x 0 , y 0 , z 0 ) , the slope of its vertical cross sections in the positive x -direction is m 1 , and the slope of its vertical cross sections in the positive y -direction is m 2 (Figure 4). Then the plane has the equation z = z 0 + m 1 ( x - x 0 ) + m 2 ( y - y 0 ) . (2) The slope-intercept equation The point-slope equation FIGURE 1 FIGURE 2 Lecture notes to accompany Section 14.4 of Calculus, Early Transcendentals by Rogawski. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Math 20C. Lecture Examples. (8/17/10) Section 14.4, p. 2 Example 1 Give an equation of the plane with slope - 6 in the positive x -direction, slope 7 in the positive y -direction, and z -intercept 10. Answer:
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/31/2011 for the course MATH 20C taught by Professor Helton during the Spring '08 term at UCSD.

Page1 / 5

Rog_Sec_14_4 - Math 20C Lecture Examples Section 14.4 Linear approximations and tangent planes A function z = f(x y of two variables is linear if

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online