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

231.

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

94 Views

232.

If space straight y equals square root of log space straight x plus square root of log space straight x plus square root of log 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 1 over straight x

84 Views

233.

If space straight y square root of straight x squared plus 1 end root equals log open parentheses straight x plus square root of straight x squared plus 1 end root close parentheses comma space show space that space left parenthesis straight x squared plus 1 right parenthesis dy over dx plus xy minus 1 equals 0

77 Views

234. $If space straight e to the power of straight x plus straight e to the power of straight y equals straight e to the power of straight x plus straight y comma end exponent prove space that space dy over dx equals negative fraction numerator straight e to the power of straight x left parenthesis straight e to the power of straight y minus 1 right parenthesis over denominator straight e to the power of straight y left parenthesis straight e to the power of straight y minus 1 right parenthesis end fraction$

Here space straight e to the power of straight x plus straight e to the power of straight y equals straight e to the power of straight x plus straight y end exponent Differentiating space both space sides space straight w. straight r. straight t. space straight x comma space we space get comma bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold e to the power of bold x bold plus bold e to the power of bold y bold dy over bold dx bold equals bold e to the power of bold x bold plus bold y end exponent open parentheses bold 1 bold plus bold dy over bold dx close parentheses bold therefore bold space bold space bold space bold space bold space bold space bold space bold e to the power of bold x bold plus bold e to the power of bold y bold dy over bold dx bold equals bold e to the power of bold x bold plus bold y end exponent bold plus bold e to the power of bold x bold plus bold y end exponent bold dy to the power of bold 1 over bold dx bold therefore bold space bold left parenthesis bold e to the power of bold x bold minus bold e to the power of bold x bold plus bold y end exponent bold right parenthesis bold dy over bold dx bold equals bold e to the power of bold x bold plus bold y end exponent bold minus bold e to the power of bold x bold therefore bold space bold left parenthesis bold e to the power of bold y bold minus bold e to the power of bold x bold. bold e to the power of bold x bold right parenthesis bold dy over bold dx bold equals bold e to the power of bold x bold. bold e to the power of bold y bold minus bold e to the power of bold x bold therefore bold space bold space bold space bold e to the power of bold y bold left parenthesis bold 1 bold minus bold e to the power of bold x bold right parenthesis bold dy over bold dx bold equals bold e to the power of bold x bold left parenthesis bold e to the power of bold y bold minus bold 1 bold right parenthesis bold therefore bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold dy over bold dx bold equals fraction numerator bold e to the power of bold x bold left parenthesis bold e to the power of bold y bold minus bold 1 bold right parenthesis over denominator bold e to the power of bold y bold left parenthesis bold 1 bold minus bold e to the power of bold x bold right parenthesis end fraction bold therefore bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold dy over bold dx bold equals bold minus fraction numerator bold e to the power of bold x bold left parenthesis bold e to the power of bold y bold minus bold 1 bold right parenthesis over denominator bold e to the power of bold y bold left parenthesis bold e to the power of bold x bold minus bold 1 bold right parenthesis end fraction

73 Views

235.

If space straight y equals straight x plus fraction numerator 1 over denominator straight x plus begin display style fraction numerator 1 over denominator straight x plus... end fraction end style end fraction comma space prove space that space dy over dx equals fraction numerator straight y over denominator 2 straight y minus straight x end fraction.

85 Views

236.

If space straight x square root of 1 plus straight y end root plus straight y square root of 1 plus straight x end root equals 0 comma space show space that space dy over dx equals negative left parenthesis 1 plus straight x right parenthesis to the power of negative 2 end exponent

78 Views

237.

If space space ax squared plus 2 hxy plus by squared space equals space 1 comma space verify space that space dy over dx cross times dx over dy equals 1

74 Views

238. Differentiate x^x w.r.t.x.

89 Views

239.

Differentiate (a^x)^x w.r.t.x.

83 Views

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

open parentheses 1 over straight x close parentheses to the power of straight x

84 Views