Problems on Radius of Curvature Problem No 10 - Application of Derivatives - Diploma Maths - II | Summary and Q&A

45 views
April 11, 2022
by
Ekeeda
YouTube video player
Problems on Radius of Curvature Problem No 10 - Application of Derivatives - Diploma Maths - II

TL;DR

Find the radius of curvature of the curve y = log(sin x) at x = pi/2, which is equal to -1.

Install to Summarize YouTube Videos and Get Transcripts

Key Insights

  • 🎮 In this video, the problem of finding the radius of curvature is solved for a given curve.
  • 📏 The chain rule is used to find the derivative of the function.
  • ❓ The second derivative is calculated by differentiating the first derivative.
  • ❓ The formula for radius of curvature involves the first and second derivatives of the function.
  • 💠 The radius of curvature is found to be -1 unit, indicating a concave shape.
  • ☺️ The value of the first derivative at x = pi/2 is 0, indicating a horizontal tangent.
  • ☺️ The value of the second derivative at x = pi/2 is -1, showing concavity.

Transcript

Read and summarize the transcript of this video on Glasp Reader (beta).

Questions & Answers

Q: What is the given curve and what is required to be found?

The given curve is y = log(sin x), and we need to find the radius of curvature at x = pi/2.

Q: How is the derivative of the given function calculated?

The derivative of y = log(sin x) is found using the chain rule, giving us dy/dx = cot x.

Q: What is the second derivative of the function?

The second derivative of y = log(sin x) is d^2y/dx^2 = -cosec^2 x.

Q: How is the radius of curvature calculated?

The formula for the radius of curvature is (1 + (dy/dx)^2)^(3/2) / |d^2y/dx^2|. By substituting the previously found values, the radius of curvature is determined to be -1 unit.

Summary & Key Takeaways

  • The problem involves finding the radius of curvature of a curve represented by y = log(sin x) at x = pi/2.

  • The derivative of the function is calculated using the chain rule, resulting in dy/dx = cot x.

  • The second derivative of the function is found to be d^2y/dx^2 = -cosec^2 x.

  • The formula for the radius of curvature is applied, resulting in a radius of curvature of -1 unit.

Share This Summary 📚

Summarize YouTube Videos and Get Video Transcripts with 1-Click

Download browser extensions on:

Explore More Summaries from Ekeeda 📚

Summarize YouTube Videos and Get Video Transcripts with 1-Click

Download browser extensions on: