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Application of Derivatives

Name: Zigya - For The Curious Learner
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Short Answer Type

361.

Use differentials to approximate:
$square root of 3.968 end root$

92 Views

362.

Use differentials to approximate:
$square root of 25.2 end root$

82 Views

363.

Use differentials to approximate:
$left parenthesis 0.0037 right parenthesis to the power of 1 half end exponent$

75 Views

364.
Use differentials to approximate:
$square root of 36.3 end root$

Take $straight y space equals space square root of straight x comma space space space space straight x space equals space 36 comma space space space dx space equals space δx equals 0.3 space space space space so space that space space straight x space plus space δx space equals space 36.3$
Now, $straight y plus δy space equals space square root of straight x plus δx end root$
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$and space dy space equals space dy over dx dx space equals space fraction numerator 1 over denominator 2 square root of straight x end fraction dx space equals space fraction numerator 1 over denominator 2 square root of 36 end fraction left parenthesis 0.3 right parenthesis space equals space fraction numerator 0.3 over denominator 12 end fraction space equals space 0.025 therefore space space space space from space left parenthesis 1 right parenthesis comma space space space space space square root of 36.3 end root space equals space 0.025 plus 6 space equals space 6.025$