Use differentials, find the approximate value of each of the fol

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Application of Derivatives

Short Answer Type

381.

Use differentials to approximate fourth root of $17 over 81$ .

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382.

Use differentials, find the approximate value of each of the following upto 3 places of decimal:
$left parenthesis 31.9 right parenthesis to the power of 1 fifth end exponent$

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383.

Use differentials, find the approximate value of each of the following upto 3 places of decimal:
$left parenthesis 0.999 right parenthesis to the power of 1 over 10 end exponent$

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384.

Use differentials, find the approximate value of each of the following upto 3 places of decimal:
$left parenthesis 32.15 right parenthesis to the power of 1 fifth end exponent$

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385.
Use differentials, find the approximate value of each of the following upto 3 places of decimal:
$left parenthesis 33 right parenthesis to the power of negative 1 fifth end exponent$

left parenthesis 33 right parenthesis to the power of negative 1 fifth end exponent space equals space fraction numerator 1 over denominator left parenthesis 33 right parenthesis to the power of begin display style 1 fifth end style end exponent end fraction

Let space space straight y space equals space straight f left parenthesis straight x right parenthesis space equals space straight x to the power of 1 fifth end exponent comma space space space space straight x space equals space 32 comma space space space dx space equals space 1

straight f left parenthesis straight x plus increment straight x right parenthesis space equals space left parenthesis 33 right parenthesis to the power of 1 fifth end exponent space equals space straight f left parenthesis straight x right parenthesis space plus space increment straight y space equals space 2 space plus space dy over dx cross times dy space space space space space space space space space space space space space space space space space space equals space 2 plus fraction numerator 1 over denominator 5 straight x to the power of begin display style 4 over 5 end style end exponent end fraction cross times 1 space equals space 2 plus fraction numerator 1 over denominator 5 space cross times space left parenthesis 32 right parenthesis to the power of begin display style 4 over 5 end style end exponent end fraction space space space space space space space space space space space space space space space space equals 2 plus fraction numerator 1 over denominator 5 space cross times space 16 end fraction space equals space 2 plus 1 over 80 space equals space 161 over 80 space space space space space space space space space space space space space space space space open parentheses 1 over 33 close parentheses to the power of 1 fifth end exponent space equals fraction numerator 1 over denominator left parenthesis 33 right parenthesis to the power of begin display style 1 fifth end style end exponent end fraction space equals fraction numerator 1 over denominator begin display style 161 over 80 end style end fraction space equals space 80 over 161 space equals space 0.4968 space equals space 0.497

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386.

If y = x⁴ – 10 and if x changes from 2 to 1.99, what is the approximate change in y?

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387. If y = x⁴ + 10 and x changes from 2 to 1.99, find the approximate change in y.

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388.

Find the approximate value of f (2.01), where f (x) = 4x² + 5x + 2 .

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389.

Find the approximate value of f (5.001), where f (x) = x³ –7x² + 15.

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390.

Find the approximate value of f(3.02), where f (x) = 3x² + 5x + 3 .

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