4.7.1 Many
improper integrals can be evaluated by comparing functions with the
method of leading behavior. State which of the given pair of functions
approaches its limit more quickly, and demonstrate the result with L’H
ˆopital’s rule when needed. Which function approaches 0 faster as x approaches infinity: ...
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4.7.2 Many
improper integrals can be evaluated by comparing functions with the
method of leading behavior. State which of the given pair of functions
approaches its limit more quickly, and demonstrate the result with L’H
ˆopital’s rule when needed. Which function approaches 0 faster as x
approaches infinity: ...
Get solution
4.7.3 Many
improper integrals can be evaluated by comparing functions with the
method of leading behavior. State which of the given pair of functions
approaches its limit more quickly, and demonstrate the result with L’H
ˆopital’s rule when needed. Which function approaches infinity faster as
x approaches 0: ...
Get solution
4.7.4 Many
improper integrals can be evaluated by comparing functions with the
method of leading behavior. State which of the given pair of functions
approaches its limit more quickly, and demonstrate the result with L’H
ˆopital’s rule when needed. Which function approaches infinity faster as
x approaches 0: ...
Get solution
4.7.5 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.6 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.7 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.8 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.9 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.10 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.11 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.12 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.13 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.14 Evaluate the following improper integrals or say why they don’t converge. ...
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4.7.15 Use
the comparison test to deduce whether the following improper integrals
converge. If they do, find an upper bound on the value. ...
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4.7.16 Use
the comparison test to deduce whether the following improper integrals
converge. If they do, find an upper bound on the value. ...
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4.7.17 Use
the comparison test to deduce whether the following improper integrals
converge. If they do, find an upper bound on the value. ...
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4.7.18 Use
the comparison test to deduce whether the following improper integrals
converge. If they do, find an upper bound on the value. ...
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4.7.19 The
method of leading behavior can be used to deduce whether some improper
integrals converge. Choose the leading behavior of the denominator of
each function and compare with the results using the comparison test. ...
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4.7.20 The
method of leading behavior can be used to deduce whether some improper
integrals converge. Choose the leading behavior of the denominator of
each function and compare with the results using the comparison test. ...
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4.7.21 The
method of leading behavior can be used to deduce whether some improper
integrals converge. Choose the leading behavior of the denominator of
each function and compare with the results using the comparison test. ...
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4.7.22 The
method of leading behavior can be used to deduce whether some improper
integrals converge. Choose the leading behavior of the denominator of
each function and compare with the results using the comparison test. ...
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4.7.24 Compare the following series with the given integral to determine whether the sum approaches infinity. ...
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4.7.24 Compare the following series with the given integral to determine whether the sum approaches infinity. ...
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4.7.25 Compare the following series with the given integral to determine whether the sum approaches infinity. ...
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4.7.26 Compare the following series with the given integral to determine whether the sum approaches infinity. ...
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4.7.27 Write
pure-time differential equations to describe the following situations,
find out what happens over the long term, and state whether the rule
could be followed indefinitely. The volume of a cell is increasing at a rate of ..., starting from a size of 500 ...
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4.7.28 Write
pure-time differential equations to describe the following situations,
find out what happens over the long term, and state whether the rule
could be followed indefinitely. The concentration of a toxin in a cell is increasing at a rate of ...μmol/L/s, starting from a concentration of 10 μmol/L. If the cell is poisoned when the concentration exceeds 30 μmol/L, could this cell survive?
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4.7.29
Write
pure-time differential equations to describe the following situations,
find out what happens over the long term, and state whether the rule
could be followed indefinitely. A population of bacteria is increasing
at a rate of ...bacteria per hour, starting from a population of ....
Could this sort of growth be maintained indefinitely? When would the
population reach 2.0 ×...?Would you say that this population is growing quickly?
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4.7.30 Write
pure-time differential equations to describe the following situations,
find out what happens over the long term, and state whether the rule
could be followed indefinitely. A population of bacteria is increasing at a rate of ...bacteria
per hour, starting from a population of 1000. Could this sort of
growth be maintained indefinitely? Would the population reach 2000?
Get solution