Problem 4. The bell-shaped curve y = f(x) below satisfies dx = -xy. R y= f(x) a (a) Use cylindrical shells and the substitution u = R about the y-axis has the volume V = 27(1 – c), where c = f(a). Do not attempt to find an explicit function f(r) = y. f(x) to show that the solid obtained by rotating the region (b) Given that the function f(x) asymptotically approaches 0 as x → ∞, find the limiting volume as a → o.
Problem 4. The bell-shaped curve y = f(x) below satisfies dx = -xy. R y= f(x) a (a) Use cylindrical shells and the substitution u = R about the y-axis has the volume V = 27(1 – c), where c = f(a). Do not attempt to find an explicit function f(r) = y. f(x) to show that the solid obtained by rotating the region (b) Given that the function f(x) asymptotically approaches 0 as x → ∞, find the limiting volume as a → o.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:dy
Problem 4. The bell-shaped curve y = f (x) below satisfies
-xy.
d.x
R
y=f(x)
а
(a) Use cylindrical shells and the substitution u =
R about the y-axis has the volume V = 2T (1 – c), where c =
function f(x) = y.
f (x) to show that the solid obtained by rotating the region
f(a). Do not attempt to find an explicit
(b) Given that the function f(x) asymptotically approaches 0 as x → ∞, find the limiting volume as
→ 0.
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