Let f ( z ) be the branch of z 2 − 1 which is positive for large positive real values of z. Expand the square root in powers of 1 / z to obtain the Laurent series of f ( z ) about ∞ . Thus by Problem 8.1 find the residue of f ( z ) at ∞ . Check your result by using equation (8.2).
Let f ( z ) be the branch of z 2 − 1 which is positive for large positive real values of z. Expand the square root in powers of 1 / z to obtain the Laurent series of f ( z ) about ∞ . Thus by Problem 8.1 find the residue of f ( z ) at ∞ . Check your result by using equation (8.2).
Let
f
(
z
)
be the branch of
z
2
−
1
which is positive for large positive real values of z. Expand the square root in powers of
1
/
z
to obtain the Laurent series of
f
(
z
)
about
∞
.
Thus by Problem 8.1 find the residue of
f
(
z
)
at
∞
.
Check your result by using equation (8.2).
For q5.b). The answer on the mark scheme is minus phi I. But when I did it I got -2 phi I. Where did I go wrong. The mark scheme is unclear.
Let f(x)=e(x-1)^2-1/(x-1)2 for x ≠ 1 and f(1)=1
a. Write the first four nonzero terms and the general term of the Taylor series for e(x-1)^2 about x=1
b. Use the series found in (a) to write the first four nonzero terms and the general term for the Taylor series for f about x=1
c. Determine the interval of convergence for the series given in (b).
d. Use the series for f about x=1 to determine if the graph of f has any points of inflection.
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.