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

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

left parenthesis straight a plus 2 straight x right parenthesis to the power of 7 straight x end exponent

84 Views

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

left parenthesis 2 straight x plus 3 right parenthesis to the power of straight x minus 5 end exponent

86 Views

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

straight x to the power of log space straight x end exponent

81 Views

244. Differentiate the following w.r.t.x: $left parenthesis straight x to the power of straight x right parenthesis to the power of square root of straight x end exponent$

Let space straight y equals space left parenthesis straight x to the power of straight x right parenthesis to the power of square root of straight x end exponent equals straight x to the power of straight x to the power of begin inline style bevelled 3 over 2 end style end exponent end exponent therefore space log space straight y equals log space straight x to the power of straight x to the power of begin inline style begin display style 3 over 2 end style end style end exponent space space space space end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space log space straight y equals straight x to the power of begin inline style bevelled 3 over 2 end style end exponent. log space straight x Differentiating space space space both space sides space straight w. straight r. straight t. space straight x comma 1 over straight y dy over dx equals straight x to the power of 3 over 2 end exponent.1 over straight x plus left parenthesis log space straight x right parenthesis.3 over 2 straight x to the power of 1 half end exponent therefore space dy over dx equals straight y open square brackets straight x to the power of 1 half end exponent plus 3 over 2 straight x to the power of 1 half end exponent space log space straight x close square brackets equals left parenthesis straight x to the power of straight x right parenthesis to the power of square root of straight x end exponent open square brackets straight x to the power of 1 half end exponent plus 3 over 2 straight x to the power of 1 half end exponent space log space straight x close square brackets.

87 Views

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

straight x to the power of straight x to the power of straight x end exponent space space space or space straight x to the power of left parenthesis straight x to the power of straight x right parenthesis end exponent

90 Views

246. Differentiate (log x)^{log x}, x > 1 w.r.t.x.

94 Views

247. If x^y = e^{x - y}, prove that

dy over dx equals fraction numerator log space straight x over denominator left parenthesis 1 plus log space straight x right parenthesis squared end fraction

88 Views

248.

If space straight y equals straight x to the power of straight x to the power of straight x........ infinity end exponent end exponent space prove space that space straight x dy over dx equals fraction numerator straight y squared over denominator 1 minus straight y space log space straight x end fraction

91 Views

249.

If space straight y equals straight e to the power of straight x plus straight e to the power of straight x plus straight e to the power of straight x plus........ infinity end exponent end exponent comma space show space that space dy over dx equals fraction numerator straight y over denominator 1 minus straight y end fraction.

82 Views

250.

If space straight y equals straight a to the power of straight a to the power of straight a to the power of straight a........... infinity end exponent end exponent end exponent comma prove space that space dy over dx equals fraction numerator straight y squared log space straight y over denominator straight x left parenthesis 1 minus straight y space log space straight x. log space straight y right parenthesis end fraction

92 Views