A magnetic field, B, is given as a function of the distance, r, from the center of a wire as follows. - Bo for r ≤ ro To B(r) = ro Bo for r>ro Bo TALA (a) Sketch a graph of B against r. B Bo B Bo To To O B is continuous at r = ro, because lim_ B(r) = Bo and r-ro B B Bo What is the meaning of the constant Bo? O The constant Bo is the value of B when r>ro and indicates the end behavior of B. O The constant Bo is the value of B at r = ro and the maximum value of B. O The constant Bo is always exactly equal to the value of ro and is the maximum value of B. O The constant Bo is the value of B at r = ro and the minimum value of B. O The constant Bo is always exactly equal to the value of ro and is the minimum value of B. lim_B(r) = -Bo and r-ro (b) Is B continuous at r = ro? Give reasons. OB is continuous at r = ro, because lim_B(r) = 1.5B and lim_B(r) = Bo rro r-ro lim_ B(r) = Bo. O B is continuous at r = ro, because lim_ B(r) = Bo. r-rot OB is not continuous at r = ro, because lim_B(r) = -Bo and r-ro B is not continuous at r = ro, because lim B(r) = Bo and lim, B(r) = -Bo. r+ro r-ro lim_ B(r) = Bo. r-rot To To (c) Is B differentiable at r = ro? Give reasons. O The function B is differentiable at r = ro, because the graph does not have a corner at r = ro and the slope for r < ro is equal to the s
A magnetic field, B, is given as a function of the distance, r, from the center of a wire as follows. - Bo for r ≤ ro To B(r) = ro Bo for r>ro Bo TALA (a) Sketch a graph of B against r. B Bo B Bo To To O B is continuous at r = ro, because lim_ B(r) = Bo and r-ro B B Bo What is the meaning of the constant Bo? O The constant Bo is the value of B when r>ro and indicates the end behavior of B. O The constant Bo is the value of B at r = ro and the maximum value of B. O The constant Bo is always exactly equal to the value of ro and is the maximum value of B. O The constant Bo is the value of B at r = ro and the minimum value of B. O The constant Bo is always exactly equal to the value of ro and is the minimum value of B. lim_B(r) = -Bo and r-ro (b) Is B continuous at r = ro? Give reasons. OB is continuous at r = ro, because lim_B(r) = 1.5B and lim_B(r) = Bo rro r-ro lim_ B(r) = Bo. O B is continuous at r = ro, because lim_ B(r) = Bo. r-rot OB is not continuous at r = ro, because lim_B(r) = -Bo and r-ro B is not continuous at r = ro, because lim B(r) = Bo and lim, B(r) = -Bo. r+ro r-ro lim_ B(r) = Bo. r-rot To To (c) Is B differentiable at r = ro? Give reasons. O The function B is differentiable at r = ro, because the graph does not have a corner at r = ro and the slope for r < ro is equal to the s
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:A magnetic field, B, is given as a function of the distance, r, from the center of a wire as follows.
- Bo
for r ≤ ro
B(r) =
Bo
Tato
kk
Bo
(a) Sketch a graph of B against r.
B
Bo
To
ro Bo for r>ro
B
Bo
To
To
(b) Is B continuous at r = ro? Give reasons.
OB is continuous at r = ro, because
B
What is the meaning of the constant Bo?
O The constant Bo is the value of B when r>ro and indicates the end behavior of B.
O The constant Bo is the value of B at r = ro and the maximum value of B.
O The constant Bo is always exactly equal to the value of ro and is the maximum value of B.
O The constant Bo is the value of B at r = ro and the minimum value of B.
O The constant Bo is always exactly equal to the value of ro and is the minimum value of B.
B
lim_B(r) = 1.5Bo and lim_ B(r) = Bo.
r-ro
r-ro
O B is continuous at r = ro, because
OB is not continuous at r = ro, because lim_B(r) = -Bo and
r+ro
B is not continuous at r = ro, because lim B(r) = Bo and
r+ro
r-ro
O B is continuous at r = ro, because lim_ B(r) = Bo and lim_ B(r) = Bo.
r-rot
lim_B(r) = -Bo and lim_ B(r) = Bo.
r-rot
r-ro
lim_ B(r) = Bo.
r-rot
lim, B(r) = -Bo.
r-ro
To
To
(c) Is B differentiable at r = ro? Give reasons.
O The function B is differentiable at r = ro, because the graph does not have a corner at r = ro and the slope for r < ro is equal to the slope for r > ro.
O The function B is differentiable at r = ro, because the function is continuous at r = ro.
O The function B is not differentiable at r = ro, because the function is not continuous at r = ro.
O The function B is not differentiable at r = ro, because the graph has a corner at r = ro and the slope is positive for r < ro and negative for r > ro.
O The function B is not differentiable at r = ro, because the function is not defined at r = ro.
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