(a)
The approximation of P+sin P
(a)
Answer to Problem 45E
This is accurate to more than 6 decimals places
Explanation of Solution
Given information:
Let P be an approximation of
Formula used:
Sin value is calculated.
Calculation:
Let’s take approximate value of
This is accurate to more than 6 decimals places
Conclusion:
This is accurate to more than 6 decimals places
(b)
the value of x using theRemainder Estimation Theorem and the Maclaurin series
(b)
Answer to Problem 45E
The value is
Explanation of Solution
Given information:
Use the Remainder Estimation Theorem and the Maclaurin series for sin x
Formula used:
Calculation:
Let P = g + x where x the error is in the original estimate
Then,
The given function is
Then,
Using Remainder Estimation Theorem for n = 2
(Use n = 2 instead n = 1 in this way better range of x)
Since,
Now,
Therefore,
Use
Therefore,
Hence, from equation (1) and (2)
Conclusion:
The value is
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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