Evaluation the radius of curvature
Not what you're looking for?
Curvature (III)
Differential Calculus
Evaluate the radius of curvature at any point (x,y) for the curves :
(a) xy = c2 (b) y = (1/2)a(ex/a + e-x/a)
See attached file for full problem description.
Purchase this Solution
Solution Summary
This solution is comprised of a detailed explanation for finding the radius of curvature at any point of the curves.
It contains step-by-step explanation for finding the radius of curvature at any point (x,y) for the curves :
(a) xy = c2 (b) y = (1/2)a(ex/a + e-x/a)
Solution contains detailed step-by-step explanation.
Solution Preview
Please see the attached file.
Curvature (III)
Differential Calculus
Written by :- Thokchom Sarojkumar Sinha
Evaluate the radius of curvature at any point (x,y) for the curves :
(a) xy = c2 (b) y = (1/2)a(ex/a + e-x/a)
Solution :- (a) xy = c2
Differentiating the equation with respect to 'x' , we get
y + x dy/dx = 0 --------------------------------------(1)
or, y + xy1 = 0 where y1 = dy/dx
or, xy1 = - y or, y1 = - y/x ------------------------------(1a)
Again differentiating (1) with respect to 'x' , we get
dy/dx + 1.dy/dx + x d2y/dx2 = 0
or, 2dy/dx + xd2y/dx2 = 0 or, 2y1 + xy2 = 0 where y1 = dy/dx , y2 = d2y/dx2
or, 2.(-y/x) + xy2 = 0 by using the relation y1 = - y/x
or, - 2y/x + xy2 = 0 or, xy2 = 2y/x
or, y2 = 2y/x2 ...
Education
- BSc, Manipur University
- MSc, Kanpur University
Recent Feedback
- "Thanks this really helped."
- "Sorry for the delay, I was unable to be online during the holiday. The post is very helpful."
- "Very nice thank you"
- "Thank you a million!!! Would happen to understand any of the other tensor problems i have posted???"
- "You are awesome. Thank you"
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.