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.

Continuity and Differentiability

Short Answer Type

321.

If space straight y equals sin open square brackets square root of sin square root of straight x end root close square brackets comma space where space straight x greater than 0 comma space find space dy over dx

83 Views

322. If y = a sin x + b cos x, prove that

straight y squared plus open parentheses dy over dx close parentheses squared equals straight a squared plus straight b squared

74 Views

323.

If space straight y equals square root of cos space straight x plus square root of cos space straight x plus square root of cos space straight x plus.... infinity end root end root end root comma space prove space that space space left parenthesis 2 straight y minus 1 right parenthesis dy over dx equals negative sin space straight x

79 Views

324.

If space straight y equals square root of sin space straight x plus square root of sin space straight x plus square root of sin space straight x plus.... infinity end root end root end root comma space prove space that space left parenthesis 2 straight y minus 1 right parenthesis dy over dx equals cos space straight x

83 Views

325.

If space straight y equals square root of tan space straight x plus square root of tan space straight x plus square root of tan space straight x plus... infinity end root end root end root comma space prove space that space left parenthesis 2 straight y minus 1 right parenthesis dy over dx equals sec squared straight x.

84 Views

326. $If space straight y equals fraction numerator sin space straight x over denominator 1 plus begin display style fraction numerator cos space straight x over denominator 1 plus begin display style fraction numerator sin space straight x over denominator 1 plus begin display style fraction numerator cos space straight x over denominator 1 plus.... infinity end fraction end style end fraction end style end fraction end style end fraction comma space prov e space that space dy over dx equals fraction numerator left parenthesis 1 plus straight y right parenthesis cos space straight x plus straight y space sin space straight x over denominator 1 plus 2 straight y plus cos space straight x minus sin space straight x end fraction$

Here space straight y equals fraction numerator sin space straight x over denominator 1 plus begin display style fraction numerator cos space straight x over denominator 1 plus begin display style fraction numerator sin space straight x over denominator 1 plus begin display style fraction numerator cos space straight x over denominator 1 plus.... infinity end fraction end style end fraction end style end fraction end style end fraction therefore space space space space space space straight y equals fraction numerator sin space straight x over denominator 1 plus begin display style fraction numerator cos space straight x over denominator 1 plus straight y end fraction end style end fraction space rightwards double arrow space straight y equals fraction numerator left parenthesis 1 plus straight y right parenthesis sin space straight x over denominator 1 plus straight y plus cos space straight x end fraction rightwards double arrow space straight y plus straight y squared plus straight y space cos space straight x equals left parenthesis 1 plus straight y right parenthesis sin space straight x Differntiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space space space space space dy over dx plus 2 straight y dy over dx plus straight y left parenthesis negative sin space straight x right parenthesis plus cos space straight x dy over dx equals left parenthesis 1 plus straight y right parenthesis cos space straight x plus sin space straight x. dy over dx therefore space left parenthesis 1 plus 2 straight y plus cos space straight x minus sin space straight x right parenthesis dy over dx equals left parenthesis 1 plus straight y right parenthesis cos space straight x plus straight y space sin space straight x therefore space dy over dx equals fraction numerator left parenthesis 1 plus straight y right parenthesis cos space straight x plus straight y space sin space straight x over denominator 1 plus 2 straight y plus cos space straight x minus sin space straight x end fraction

87 Views

327. Differentiate the following w.r.t.x:

square root of fraction numerator 1 minus cos space straight x over denominator 1 plus cos space straight x end fraction end root

86 Views

328. Differentiate the following w.r.t.x:

square root of fraction numerator sec minus 1 over denominator sec plus 1 end fraction end root

86 Views

329. Differentiate the following w.r.t.x:

fraction numerator sin space straight x over denominator 1 plus cos space straight x end fraction

83 Views

330. Differentiate the following w.r.t.x:

fraction numerator 1 minus cos space straight x over denominator sin space straight x end fraction

79 Views