Chapter 11: Q. 33 (page 889)

In Exercises 31–35 find the curvature of the given function at the indicated value of x. Then sketch the curve and the osculating circle at the indicated point.
$y = \csc x, x = \frac{π}{2}$

Short Answer

Expert verified

The curvature is $1 .$

Step by step solution

Step 1. Given information.

The given function is $y = \csc x, x = \frac{π}{2} .$

Step 2. Curvature.

Curvature is given by,

$k = \frac{|f^{''} (x)|}{{(1 + {(f^{'} (x))}^{2})}^{\frac{3}{2}}} f^{'} (x) = - \csc x \cot x f^{''} (x) = - \csc^{3} x - \cot^{2} x \csc x k = \frac{|- \csc^{3} x - \cot x \csc x|}{{(1 + (- \csc x \cot x)^{2})}^{\frac{3}{2}}} At x = \frac{π}{2}, \csc x = 1 and \cot x = 0 .then k = \frac{| - 1 |}{1} k = 1$

Step 3. Graph.

The graph will be,

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In Exercises 31–35 find the curvature of the given function at the indicated value of x. Then sketch the curve and the osculating circle at the indicated point.
$y = \csc x, x = \frac{π}{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Curvature.

Step 3. Graph.

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In Exercises 31–35 find the curvature of the given function at the indicated value of x. Then sketch the curve and the osculating circle at the indicated point.y=cscx,x=π2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Curvature.

Step 3. Graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Exercises 31–35 find the curvature of the given function at the indicated value of x. Then sketch the curve and the osculating circle at the indicated point.
$y = \csc x, x = \frac{π}{2}$