Self Studies

Limits and Deri...

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  • Question 1
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    Value of limx01+tanx 31tanx 3 x\underset { x\rightarrow 0 }{ lim } \dfrac { \sqrt [ 3 ]{ 1+\tan { x }  } -\sqrt [ 3 ]{ 1-\tan { x }  }  }{ x } is

  • Question 2
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    Ltx0(1+sinx)cotx=\underset { x\rightarrow 0 }{ Lt } (1+sin\quad x)^{ cot\quad x }= 

  • Question 3
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    limx0(cosecx) 1logx \underset { x\rightarrow 0 }{ lim } { \left( cosecx \right)  }^{ \dfrac { 1 }{ logx }  } is equal to

  • Question 4
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    limx01e2tan(π 4+x)1/x\underset { x\rightarrow 0 }{ lim } \dfrac { 1 }{ { e }^{ 2 } } tan\left( \dfrac { \pi  }{ 4 } +x \right) ^{ 1/x }

  • Question 5
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    If cosy=xcos(a+y)anddydx=k1+x22xcosacosy=xcos(a+y)and\quad \cfrac { dy }{ dx } =\cfrac { k }{ 1+{ x }^{ 2 }-2xcosa } then find value of k?

  • Question 6
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    limx0(1+tanx1+sinx )cosecx\underset { x\rightarrow 0 }{ lim } \left( \dfrac { 1+tanx }{ 1+sinx }  \right) ^{ cosecx } is equal to

  • Question 7
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    limx11+sinπ(3x1+x2)1+cosπx\lim_{x\rightarrow 1}\dfrac {1+\sin \pi\left(\dfrac {3x}{1+x^{2}}\right)}{1+\cos \pi x} is equal to

  • Question 8
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    limx0x([x]+x)sin[x]xlim_{x \to 0^-} \dfrac{x([x]+ \mid x \mid )sin[x]}{\mid x \mid} is equal to

  • Question 9
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    limxπ2(1+cosx1cosx)secx=\lim _ { x \rightarrow \frac { \pi } { 2 } } \left( \frac { 1 + \cos x } { 1 - \cos x } \right) ^ { \sec x } =

  • Question 10
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    The value of  limx(x2+x)log(xcot1x)\displaystyle \lim _{ x\rightarrow \infty } (|x^{2}|+x)\log{(x\cot^{-1}{x})} is :

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