JEE Main & Advanced Mathematics Differentiation Question Bank

done Numerical Value Type Questions - Limits and Derivatives Total Questions - 15

• question_answer1)
  \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\,\frac{x\cot \left( 4x \right)}{{{\sin }^{2}}x{{\cot }^{2}}\left( 2x \right)}\] is equal to
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• question_answer2)
  \[\underset{x\to {}^{\pi }/{}_{4}}{\mathop{\lim }}\,\frac{{{\cot }^{3}}x-\tan x}{\cos \left( x+{}^{\pi }/{}_{4} \right)}\] is
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• question_answer3)
  \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\sin }^{2}}x}{\sqrt{2}-\sqrt{1+\cos x}}\] equal to \[a\sqrt{2},\] then a is
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• question_answer4)
  \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{\tan \,2x-x}{3x-\sin x}=\]
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• question_answer5)
  \[\underset{h\to 0}{\mathop{\lim }}\,\,\,\,\frac{f(2h+2+{{h}^{2}})-f(2)}{f(h-{{h}^{2}}+1)-f(1)},\] given that \[f'(2)=6\]and \[f'(1)=4\] is equal to
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• question_answer6)
  \[\underset{x\to \pi /2}{\mathop{\lim }}\,\left[ x\tan x-\left( \frac{\pi }{2} \right)\sec x \right]=-a,\] then a is
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• question_answer7)
  Let \[f(x)=\sqrt{x-1}+\sqrt{x+24-10\sqrt{x-1}};\]\[1<x<26\] be real valued function. Then \[f'(x)\] for \[1<x<26\] is
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• question_answer8)
  The value of the derivative of \[|x-1|+|x-3|\] at \[x=2\] is
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• question_answer9)
  The value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\left[ \frac{a}{x}-\cot \frac{x}{a} \right]\] is
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• question_answer10)
  Let \[f(x)=4\] and \[f'(x)=4\]. If \[\underset{x\to 2}{\mathop{\lim }}\,\,\,\,\frac{xf\,\,(2)-2f\,(x)}{x-2}=-a.\] then a is
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• question_answer11)
  \[\underset{x\to \frac{\pi }{2}}{\mathop{\lim }}\,\,\,\frac{\left[ 1-\tan \left( \frac{x}{2} \right) \right]\,[1-\sin x]}{\left[ 1+\tan \left( \frac{x}{2} \right) \right]\,{{[\pi -2x]}^{3}}}\] is \[\frac{1}{{{2}^{p}}},\] then p=
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• question_answer12)
  Let \[f:\,\,R\to R\] be a differentiable function satisfying \[f'(3)+f'(2)=0.\] Then \[\underset{x\to 0}{\mathop{\lim }}\,\,\,{{\left( \frac{1+f(3+x)-f(3)}{1+f(2-x)-f(2)} \right)}^{\frac{1}{x}}}\] is
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• question_answer13)
  If \[\underset{x\to 1}{\mathop{\lim }}\,\frac{{{x}^{4}}-1}{x-1}=\underset{x\to k}{\mathop{\lim }}\,\frac{{{x}^{3}}-{{k}^{3}}}{{{x}^{2}}-{{k}^{2}}},\] then value of k up to two decimal places is
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• question_answer14)
  If \[\underset{x\to 1}{\mathop{\lim }}\,\,\frac{{{x}^{2}}-ax+b}{x-1}=5\] and \[a+b\] is equal to \[-c,\] then value of c is
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• question_answer15)
  The value of \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\frac{x\cos x-\log (1+x)}{{{x}^{2}}}\] is
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