Order of a difference equation.
The order of a difference equation refers to the highest difference in the equation, representing the number of steps (or lag) between the variables. In simple terms, it is the highest value of \( k \) in _____ ____ ________ ____ ________ ________ __________ __________ ______ _____ ______.
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Consider the fishing optimal control problem defined by
where is the fish population at time
, and
is the fishing intensity or catch (
and
are constants). If
is the discount rate, the objective function is given by
where the utility of consumption is .
a) State the transversality condition.
b) Find the optimal consumption , if
.
Homogeneous and Homothetic functions.
Let be the functional defined by
with boundary conditions and
. Find the extremals in the interval
.
b) Find the extremals for
subject to and
.
क्रैमर-राव असमानता
समघात और व्यवस्थित फलन
In a random sample of 400 university students, 300 failed the examination. In another sample of 500 affiliated college students, 300 failed the same examination. Find the standard error (S.E.) of the difference between the proportion of failures:
i) In university departments.
ii) Between university departments and affiliated colleges.
For the function :
i) Find the linear and quadratic approximations.
ii) Derive the Maclaurin series expansion.
b) Let be defined as
Find the Jacobian at the point
.