If y = f(x) is a continuous curve and can be made x = f(y) then, A. its arc length can always be determined in both expressions using the same limi B. its default area is the region under it. C. its volume is determined by rotating it to any axis of revolution. D. its definite integral is positive in both expressions. The solid formed by moving a cross sectional area perpendicular to x-axis A. will always have its base parallel to x-axis B. will always have its base parallel to y-axis C. will produce an incremental change along x-axis

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hello. Please help me pick the correct letter/s (It could be more than 1) of the correct answer/s. If none of the above, pick E. And if possible, can you please explain why? Thank you.

4. Suppose a function y = f(x) is so be revolved at x = e from point (a, b) to (c, d), what is the correct expression of
the surface of revolution provided that the equation is continuous along the limits of integration?
A. 2r(x)/1+[f'(x)]² dx
В.
B. 27(x – e)/1+ [f"()]² dx
c. | 2nf(y)/1+[f')]* dy
D. 2n(e – x)/1+ [f'(x)]² dx
5. Which of these conditions fall/falls under washer method?
A. The area to be revolved is an area between two curves.
B. The incremental change of the element used is parallel to the axis of revolution.
C. The area under a curve is continuous and is revolved using the element perpendicular to axis of revolution.
D. No part of the area between two curves touches the axis of revolution.
Transcribed Image Text:4. Suppose a function y = f(x) is so be revolved at x = e from point (a, b) to (c, d), what is the correct expression of the surface of revolution provided that the equation is continuous along the limits of integration? A. 2r(x)/1+[f'(x)]² dx В. B. 27(x – e)/1+ [f"()]² dx c. | 2nf(y)/1+[f')]* dy D. 2n(e – x)/1+ [f'(x)]² dx 5. Which of these conditions fall/falls under washer method? A. The area to be revolved is an area between two curves. B. The incremental change of the element used is parallel to the axis of revolution. C. The area under a curve is continuous and is revolved using the element perpendicular to axis of revolution. D. No part of the area between two curves touches the axis of revolution.
Choose the letter(s) of the correct answer. Choose E if none of the choices corresponds to the correct answer.
1. If y = f(x) is a continuous curve and can be made x = f(y) then,
A. its arc length can always be determined in both expressions using the same limits of integration.
B. its default area is the region under it.
C. its volume is determined by rotating it to any axis of revolution.
D. its definite integral is positive in both expressions.
2. The solid formed by moving a cross sectional area perpendicular to x-axis
A. will always have its base parallel to x-axis
B. will always have its base parallel to y-axis
C. will produce an incremental change along x-axis
D. will produce an incremental change along y-axis
3. If a circle with center (h, k) and radius R is made as a base of a solid formed by infinitely many semi-circles of radius
r, then
A. the radius r of any semi-circle is k +R.
B. the general equation of the area to be integrated becomes 0.5tR?.
C. the radius of any semi-circle is R² – (y – k)² + h.
D. the radius of any semi-circle is /R² – (x – h)² + k.
Transcribed Image Text:Choose the letter(s) of the correct answer. Choose E if none of the choices corresponds to the correct answer. 1. If y = f(x) is a continuous curve and can be made x = f(y) then, A. its arc length can always be determined in both expressions using the same limits of integration. B. its default area is the region under it. C. its volume is determined by rotating it to any axis of revolution. D. its definite integral is positive in both expressions. 2. The solid formed by moving a cross sectional area perpendicular to x-axis A. will always have its base parallel to x-axis B. will always have its base parallel to y-axis C. will produce an incremental change along x-axis D. will produce an incremental change along y-axis 3. If a circle with center (h, k) and radius R is made as a base of a solid formed by infinitely many semi-circles of radius r, then A. the radius r of any semi-circle is k +R. B. the general equation of the area to be integrated becomes 0.5tR?. C. the radius of any semi-circle is R² – (y – k)² + h. D. the radius of any semi-circle is /R² – (x – h)² + k.
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