a. Explanation Given information: The length integral is L = ∫ 1 2 1 + 1 y 4 d y . The curve passes through the point ( 0 , 1 ) . Calculation: Show the length of integral as follows: L = ∫ 1 2 1 + 1 y 4 d y (1) The expression to find the length of the curve x = f ( y ) on the interval [ a , b ] is shown as follows: L = ∫ a b 1 + ( d x d y ) 2 d y (2) Compare Equation (1) and Equation (2). ( d x d y ) 2 = 1 y 4 Take square root on both the sides b. To determine Find the number of curves in the function y = 1 1 − x .

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Chapter 6.3, Problem 22E

To determine

Find a curve that passes through the given point (0,1) with a positive derivative.

To determine

Find the number of curves in the function y=11−x.

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Chapter 6.3, Problem 21E

Chapter 6.3, Problem 23E

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Find a curve that passes through the given point ( 0 , 1 ) with a positive derivative.