from Mathematics Continuity and Differentiability

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.

Advertisement

Continuity and Differentiability

Short Answer Type

481.

Prove space that space dy over dx space is space independent space of space straight x comma space when straight y equals cot to the power of negative 1 end exponent open square brackets fraction numerator square root of 1 plus sin space straight x end root plus square root of 1 minus sin space straight x end root over denominator square root of 1 plus sin space straight x end root minus square root of 1 minus sin space straight x end root end fraction close square brackets comma space open parentheses 0 less than straight x less than straight pi over 2 close parentheses.

81 Views

482.

Differentiate colon space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus sin space straight x end root plus square root of 1 minus sin space straight x end root over denominator square root of 1 plus sin space straight x end root minus square root of 1 minus sin space straight x end root end fraction close parentheses space straight w. straight r. straight t. straight x.

91 Views

483.

Differentiate space colon space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus straight x end root minus square root of 1 minus straight x end root over denominator square root of 1 plus straight x end root plus square root of 1 minus straight x end root end fraction close parentheses space straight w. straight r. straight t. straight x.

76 Views

484. If y = tan^-1

open parentheses fraction numerator straight x to the power of begin display style 1 third end style end exponent plus straight a to the power of begin display style 1 third end style end exponent over denominator 1 minus straight x to the power of begin display style 1 third end style end exponent space straight a to the power of begin display style 1 third end style end exponent end fraction close parentheses

when 0 < a x < 1, prove that

dy over dx

is independent of a.

95 Views

Advertisement

485.

straight y equals sin to the power of negative 1 end exponent open curly brackets straight x square root of 1 minus straight x end root minus square root of straight x square root of 1 minus straight x squared end root close curly brackets space semicolon space find space dy over dx comma

72 Views

Advertisement

486. $If space straight y equals sin to the power of negative 1 end exponent left parenthesis straight x squared square root of 1 minus straight x squared end root plus straight x square root of 1 minus straight x to the power of 4 end root right parenthesis comma space show space that space dy over dx minus fraction numerator 2 straight x over denominator square root of 1 minus straight x to the power of 4 end root end fraction equals fraction numerator 1 over denominator square root of 1 minus straight x to the power of 4 end root end fraction$

space straight y equals sin to the power of negative 1 end exponent left parenthesis straight x squared square root of 1 minus straight x squared end root plus straight x square root of 1 minus straight x to the power of 4 end root right parenthesis Put space straight x squared equals sin space straight theta comma space straight x equals sin space straight ϕ therefore space straight y equals sin to the power of negative 1 end exponent left parenthesis sin space straight theta square root of 1 minus sin squared space straight ϕ end root plus sin space straight ϕ square root of 1 minus sin squared space straight theta end root right parenthesis space space space space space space space equals sin to the power of negative 1 end exponent left parenthesis sin space straight theta space cos space straight ϕ plus cos space straight theta space sin space straight ϕ right parenthesis equals sin to the power of negative 1 end exponent left square bracket sin left parenthesis straight theta plus straight ϕ right parenthesis right square bracket therefore space straight y equals straight theta plus straight ϕ space space rightwards double arrow space straight y equals sin to the power of negative 1 end exponent space straight x squared plus sin to the power of negative 1 end exponent space straight x dy over dx equals fraction numerator 1 over denominator square root of 1 minus straight x to the power of 4 end root end fraction 2 straight x plus fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction space rightwards double arrow space dy over dx minus fraction numerator 2 straight x over denominator square root of 1 minus straight x to the power of 4 end root end fraction equals fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction

75 Views

Advertisement

487.

Differentiate space sin to the power of negative 1 end exponent open parentheses fraction numerator 2 straight x over denominator 1 plus straight x squared end fraction close parentheses space straight w. straight r. straight t. space tan to the power of negative 1 end exponent straight x.

84 Views

488.

Differentiate space colon space tan to the power of negative 1 end exponent open parentheses fraction numerator square root of 1 plus straight x squared end root over denominator straight x end fraction close parentheses space straight w. straight r. straight t. space sin to the power of negative 1 end exponent open parentheses fraction numerator 2 straight x over denominator 1 plus straight x squared end fraction close parentheses.

76 Views

Advertisement

489.

Differentiate space tan to the power of negative 1 end exponent open parentheses fraction numerator 3 straight x minus straight x cubed over denominator 1 minus 3 straight x squared end fraction close parentheses space straight w. straight r. straight t. space tan to the power of negative 1 end exponent open parentheses fraction numerator 2 straight x over denominator 1 minus straight x squared end fraction close parentheses

89 Views

490.

Differentiate space colon space cos to the power of negative 1 end exponent open parentheses fraction numerator 1 minus straight x squared over denominator 1 plus straight x squared end fraction close parentheses space straight w. straight r. straight t. space tan to the power of negative 1 end exponent open parentheses fraction numerator 3 straight x minus straight x cubed over denominator 1 minus 3 straight x squared end fraction close parentheses

82 Views

Advertisement