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Task 1. Given the function . Calculate the increment and its linear part when
changes from
to
.
The answer:
.
Task 2. Calculate the increment and the differential of the function when
and
. Calculate the absolute and relative errors as the increment is replaced by the differential.
The answer: absolute error 0,04;
relative error .
Task 3. Find the differentials of the functions:
а) ; b)
; b) 5
; c)
.
Task 4. Find the differentials of the functions: а) ; b)
.
The answer: а) ; b)
.
Task 5. Find the differentials of the functions: а) ; b)
.
Task 6. Calculate the approximate value of the function as
changes from
to
. What is the value of
?
The answer: .
Task 7. Calculate approximately: а) ; b)
.
The answer: а) ; b)
.
Завдання 8. Represent the differential of the following functionsin terms ofindependent variable and its differential:
а) ,
; б)
,
.
Answer: а) ; b)
.
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