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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

  1. (a) How do you find the slope of a tangent line to a polar curve?
  2. (b) How do you find the area of a region bounded by a polar curve?
  3. (c) How do you find the length of a polar curve ?

(a)

To determine

To find: Formula for slope of a tangent line to a polar curve.

Explanation

Calculation:

Write the formula to find the slope of a tangent line to a polar curve.

The Cartesian equation of x and y in terms of polar coordinates are as below.

x=rcosθy=rsinθ (1)

The slope of tangent is referred as dydx . Therefore, differentiate the equation (1) in terms of θ .

dydx=d(rsinθ)d(rcosθ)dy/dθdx/dθ=ddθ(rsinθ)ddθ(r<

(b)

To determine

To find: Formula for area of a region bounded by a polar curve.

(c)

To determine

To find: Formula for length of a polar curve.

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