Limits - UP Board (UPMSP) STD 11 Science MATHS Questions

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-1}\frac{\text{x}^3-3\text{x}+1}{\text{x}-1}$

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow\frac{\pi^-}{2}}\tan\text{x}$

Evaluate the following limits:
$\lim\limits_{\text{x}\rightarrow0}\frac{2\text{x}^2+3\text{x}+4}{\text{x}^2+3\text{x}+2}$

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Q 41 Marks Question1 Mark

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\sqrt{\text{x}}+\sqrt{\text{a}}}{{\text{x}+\text{a}}}$

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Q 51 Marks Question1 Mark

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow1}\frac{1+(\text{x}-1)^2}{1+{\text{x}^2}}$

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Q 62 Marks Questions2 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\tan^23\text{x}}{\text{x}^2}$

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Q 72 Marks Questions2 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{a}^\text{mx}-\text{b}^\text{nx}}{\sin\text{kx}}$

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Q 82 Marks Questions2 Marks

Evaluate the following limits:
$\lim\limits_{\text{x}\rightarrow\infty}\frac{\text{x}}{\sqrt{4\text{x}^2+1}-1}$

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Q 92 Marks Questions2 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-1}{\sqrt{1-\cos\text{x}}}$

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Q 102 Marks Questions2 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{x}-\text{x}-1}{2}$

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Q 113 Marks Question3 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\sin\text{x}^2\big(1-\cos\text{x}^2\big)}{\text{x}^6}$

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Q 123 Marks Question3 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{(\text{x}+2)^{\frac{5}{2}}-(\text{a}+2)^{\frac{5}{2}}}{\text{x}-\text{a}}$

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Q 133 Marks Question3 Marks

Evaluate the following limit:
$\lim\limits_{\text{n}\rightarrow\infty}2^{\text{n}-1}\sin\Big(\frac{\text{a}}{2^\text{n}}\Big)$

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Q 143 Marks Question3 Marks

Evaluate the following limits:
$\lim\limits_{\text{x}\rightarrow\infty}\frac{3\text{x}^{-1}+4\text{x}^{-2}}{5\text{x}^{-1}+6\text{x}^{-2}}$

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Q 153 Marks Question3 Marks

Evaluate the following limit:
Show that $\lim\limits_{\text{x}\rightarrow\infty}\big(\sqrt{\text{x}^2+\text{x}+1}-\text{x}\big)\ne\lim\limits_{\text{x}\rightarrow\infty}\big(\sqrt{\text{x}^2+1}-\text{x}\big)$

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Q 165 Marks Questions5 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{3}}}\frac{\sqrt{3}-\tan\text{x}}{\pi-3\text{x}}$

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Q 175 Marks Questions5 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow7}\frac{4-\sqrt{9+\text{x}}}{1-\sqrt{8-\text{x}}}$

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Q 185 Marks Questions5 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{1-\cos2\text{x}}{\cos2\text{x}-\cos8\text{x}}$

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Q 195 Marks Questions5 Marks

Evaluate the following limit:
If $\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{x}^{3}-\text{a}^3}{\text{x}-\text{a}}=\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^4-1}{\text{x}-1},$ find all possible value of a.

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Q 205 Marks Questions5 Marks

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-1}\frac{\text{x}^2-\text{x}-2}{\big(\text{x}^2+\text{x}\big)+\sin(\text{x}+1)}$

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Limits question types

Limits questions

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Limits MATHS - Limits

Limits question types

Limits questions

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