Q 57. Prove that the part of the polar... [FREE SOLUTION]

Chapter 9: Q 57. (page 757)

Prove that the part of the polar curve $r = \frac{1}{胃}$ that lies inside the circle defined by the polar equation r = 1 has infinite length.

Short Answer

Expert verified

It is proved that the part of the polar curve that lies inside the circle defined by the polar equation r = 1 has infinite length.

Step by step solution

Step 1. Given information

An equation of a polar curve is $r = \frac{1}{胃}$

Step 2. Explanation

Length $= {鈭�}_{1}^{鈭�} \sqrt{\frac{1}{胃^{4}} + \frac{1}{胃^{2}}} d 胃$

$= {鈭�}_{1}^{鈭�} \sqrt{\frac{1 + 胃^{2}}{胃^{4}}} d 胃 = {[\sin h^{- 1} 胃 - \frac{\sqrt{1 + 胃^{2}}}{胃}]}_{1}^{鈭�} = [\sin h^{- 1} 鈭� - \frac{\sqrt{1 + {鈭�}^{2}}}{鈭�} - \sin h^{- 1} 1 + \frac{\sqrt{1 + 1^{2}}}{1}] = 鈭�$

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Prove that the part of the polar curve $r = \frac{1}{胃}$ that lies inside the circle defined by the polar equation r = 1 has infinite length.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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91影视

Prove that the part of the polar curve r=1胃that lies inside the circle defined by the polar equation r = 1 has infinite length.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Prove that the part of the polar curve $r = \frac{1}{胃}$ that lies inside the circle defined by the polar equation r = 1 has infinite length.