Limits Archives - Noon Academy

Limits

If $f(x) = |x| - 3,find\mathop {\lim }\limits_{x \to 3} f(x)$

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{x}{{|x|}},x \ne 0\\ 0,x = 0 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} f(x) \end{array}$ does not exist.

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{|x-3|}{{(x-3)'}},x \ne 3\\ 0,x = 3 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 3} f(x) \end{array}$ does not exist.

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $f(x) = \left\{ \begin{array}{l} 1 + {x^2},0 \le x \le 1\\ 2 - x,x > 1 \end{array} \right.$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 1} f(x) \end{array}$ does not exist.

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $f(x) = \left\{ \begin{array}{l} \frac{{x - |x|}}{x},x \ne 0\\ 2,x = 0 \end{array} \right.$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} f(x) \end{array}$ does not exist.

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $f(x) = \left\{ \begin{array}{l} 5x - 4,0 < x \le 1\\ 4{x^3} - 3x,1 < x < 2 \end{array} \right.$ Find $\begin{array}{l} \mathop {\lim }\limits_{x \to 1} f(x) \end{array}$

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $f(x) = \left\{ \begin{array}{l} 4x - 5,x \le 2\\ x - a,x > 2 \end{array} \right.$ Find $\begin{array}{l} \mathop {\lim }\limits_{x \to 2} f(x) \end{array}$

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Let $f(x) = \left\{ \begin{array}{l} \frac{{3x}}{{|x| + 2x}},x \ne 0\\ 0,x = 0 \end{array} \right.$ Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} f(x) \end{array}$ does not exist.

CBSE, Class 11, Exercise 27C, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin (x/4)}}{{x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin x cos x}}{{3x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} (x\cot 2x)$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} x{\mathop{\rm cosec}\nolimits} x$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\tan x - \sin x}}{{{{\sin }^3}x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{x\cos x + \sin x}}{{{x^2} + \tan x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{({x^2} - \tan 2x)}}{{\tan x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\(tan2x - x)}}{{(3x - tanx)}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin 2x + 3x}}{{2x + sin3x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to {\raise0.7ex\hbox{$ \pi $} \!\mathord{\left/ {\vphantom {\pi 6}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$ 6 $}}} \frac{{(2{{\sin }^2}x + \sin x - 1)}}{{(2{{\sin }^2}x - 3\sin x + 1)}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sinx - 2sin3x + sin5x}}{{x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin mx}}{{tan nx}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\tan 3x}}{{sin 4x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin 4x}}{{tan 7x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\tan \alpha x}}{{\tan \beta x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\tan 3x}}{{tan 5x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin 5x}}{{sin 8x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate the following limits: $\mathop {\lim }\limits_{x \to 0} \frac{{\sin 4x}}{{6x}}$

CBSE, Class 11, Exercise 27B, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to a} \left( {\frac{{\sqrt x - \sqrt a }}{{x - a}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{h \to 0} \left( {\frac{{\sqrt x+h - \sqrt x }}{h} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{h \to 0} \frac{1}{h}\left\{ {\frac{1}{{\sqrt {x + h} }} - \frac{1}{{\sqrt x }}} \right\}$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 0} \left( {\frac{{\sqrt {1 + x} - 1}}{x}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 0} \left( {\frac{{\sqrt {2 - x} - \sqrt {2 + x} }}{x}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 2} (5 - x)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 1} (6{x^2} - 4x + 3)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^2} + 9}}{{x + 3}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^2} - 4x}}{{x - 2}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 5} \left( {\frac{{{x^2} - 25}}{{x - 5}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 1} \left( {\frac{{{x^3} - 1}}{{x - 1}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to -2} \left( {\frac{{{x^3} + 8}}{{x + 2}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^4} - 81}}{{x - 3}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 3} \left( {\frac{{{x^2} - 4x + 3}}{{{x^2} - 2x - 3}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to \frac{1}{2}} \left( {\frac{{4{x^2} - 1}}{{2x - 1}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to \ 4} \left( {\frac{{{x^3} - 64}}{{{x^2} - 16}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to \ 2} \left( {\frac{{{x^5} - 32}}{{{x^3} - 8}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to a} \left( {\frac{{{x^{\frac{5}{2}}} - {a^{\frac{5}{2}}}}}{{x - a}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to a} \left( {\frac{{{(x+2)^{\frac{5}{2}}} - {(a+2)^{\frac{5}{2}}}}}{{x - a}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

Answer:

Evaluate $\mathop {\lim }\limits_{x \to 1} \left( {\frac{{{x^n} - 1}}{{ x - 1}}} \right)$

CBSE, Class 11, Exercise 27A, Limits, Maths, RS Aggarwal

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