Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Solution 1.43 dy (a) Let be the gradient at a fixed point (x, y) on the curve, with x ≥ 0 and y ≥ 0. Then the equation of the tangent line at this point is da dy Y-y=(X-x), da where X and Y vary along the line. When X = 0, we have Y=y- dz' and the given condition then becomes dy dx 2 dy da +1=y-x- How Come??

Solution 1.43 dy (a) Let be the gradient at a fixed point (x, y) on the curve, with x ≥ 0 and y ≥ 0. Then the equation of the tangent line at this point is da dy Y-y=(X-x), da where X and Y vary along the line. When X = 0, we have Y=y- dz' and the given condition then becomes dy dx 2 dy da +1=y-x- How Come??

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
Solution 1.43 dy (a) Let be the gradient at a fixed point (x, y) on the curve, with x 20 and y > 0. Then the equation of the tangent line at this point is Y-y= dy dx -(X-x), where X and Y vary along the line. When X = 0, we have du Y=y- dx and the given condition then becomes. dy dx ² 1=y=x dy dx Come?? How Come (a) Find the family of curves for which the length of the part of the tangent between the point of contact (x, y), in the first quadrant, and the y-axis is equal to the y-coordinate of the intercept of this tangent with the y-axis. (In other words, find curves where the lengths OA and AP shown in Figure 1.10 are equal.) Figure 1.10 میرا (x, y) x
Transcribed Image Text:Solution 1.43 dy (a) Let be the gradient at a fixed point (x, y) on the curve, with x 20 and y > 0. Then the equation of the tangent line at this point is Y-y= dy dx -(X-x), where X and Y vary along the line. When X = 0, we have du Y=y- dx and the given condition then becomes. dy dx ² 1=y=x dy dx Come?? How Come (a) Find the family of curves for which the length of the part of the tangent between the point of contact (x, y), in the first quadrant, and the y-axis is equal to the y-coordinate of the intercept of this tangent with the y-axis. (In other words, find curves where the lengths OA and AP shown in Figure 1.10 are equal.) Figure 1.10 میرا (x, y) x
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS