Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Short Answer Type

381.
Use differentials to approximate fourth root of $17 over 81$ .

open parentheses 17 over 81 close parentheses to the power of 1 fourth end exponent space equals space fraction numerator left parenthesis 17 right parenthesis to the power of begin display style 1 fourth end style end exponent over denominator left parenthesis 81 right parenthesis to the power of begin display style 1 fourth end style end exponent end fraction space equals space fraction numerator left parenthesis 17 right parenthesis to the power of begin display style 1 fourth end style end exponent over denominator 3 end fraction

Let

straight f left parenthesis straight x right parenthesis space equals space straight x to the power of 1 fourth end exponent comma space space space straight x space equals space 16 comma space space dx space equals space 1 comma space space straight f left parenthesis straight x plus increment straight x right parenthesis space equals space 17 to the power of 1 fourth end exponent

increment straight y space equals space straight f left parenthesis straight x plus increment straight x right parenthesis space minus space straight f left parenthesis straight x right parenthesis

therefore space space space straight f left parenthesis straight x plus increment straight x right parenthesis space equals space straight f left parenthesis straight x right parenthesis plus increment straight y

δy

is approximately equal to dy

and space space space space space space dy space equals space dy over dx cross times dx space equals space 1 fourth straight x to the power of 3 over 4 end exponent dx space equals space fraction numerator 1 over denominator 4 straight x to the power of begin display style 3 over 4 end style end exponent end fraction cross times space dx space equals space fraction numerator 1 over denominator 4 left parenthesis 16 right parenthesis to the power of begin display style 3 over 4 end style end exponent end fraction cross times 1 space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 1 over denominator 4 space cross times 8 end fraction space equals space 1 over 32 therefore space space space space space space 17 to the power of 1 fourth end exponent space equals space 2 plus 1 over 32 space equals space 2.03125 therefore space space space space space space open parentheses 17 over 81 close parentheses to the power of 1 fourth end exponent equals space fraction numerator left parenthesis 17 right parenthesis to the power of begin display style 1 fourth end style end exponent over denominator 3 end fraction space equals space fraction numerator 2.03125 over denominator 3 end fraction space equals space 0.677083 space equals space 0.677

75 Views

382.

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

76 Views

383.

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

85 Views

384.

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

78 Views

385.

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