(a)
To find:
That there is exactly one root of the given equation and it lies between
Solution:
Yes, we could prove that there is exactly one root of the given equation and it lies between
Given:
Formulae used: The intermediate value theorem
Explanation:
Consider
For
The value of function at
Therefore,
Hence, use the formulae of intermediate value theorem
Thus, as seen from the above value
But
Conclusion: Hence there is exactly one root lie between
( b )
To find: The root of the equation to four decimal places.
Solution: 2.2079
Given: The expression is
Formulae used: The Newton nth root theorem
Explanation:
Consider
For
The value of function at
Therefore,
Hence, use the formulae of Newton nth root theorem
Therefore, various value of x given below
Conclusion: Hence the root of the expression
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Calculus (MindTap Course List)