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Recent questions tagged p160

For what value of \( \lambda \) is the function defined by \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if $ x $ \(\leq 0\)}\\ 4x + 1,& \quad \text{if $x$ > 0}\\ \end{array} \right.$ What about continuity at \( x = 1\)?

asked Aug 19, 2013 by sreemathi.v

1 answer

Discuss the continuity of the following functions $(c)\;f(x)=\sin x.\cos x$

asked May 28, 2013 by sreemathi.v

1 answer

Discuss the continuity of the following functions $(b)\;f(x)=\sin x-\cos x$

asked May 28, 2013 by sreemathi.v

1 answer

Discuss the continuity of the following functions $(a)\;f(x)=\sin x+\cos x$

asked May 28, 2013 by sreemathi.v

1 answer

Find out which of the following sentences are statements and which are not? Justify your answer

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Write down the truth value (T or F) of the following statements

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Examine the continuity of $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} \sin x - \cos x,& \quad\text{ if \(x\) \(\neq\) 0 }\\ -1 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Determine if $f$ defined by $f(x) = \left\{ \begin{array} {1 1} x^2sin \large\frac{ 1 }{x},\normalsize & \quad\text{ if x \(\neq\) 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right. $ is a continuous function?

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of \(f\), where $ f(x) = \left\{ \begin{array} {1 1} \large\frac {sinx} {x},\normalsize & \quad\text{ if \(x\) < 0 }\\ x + 1 ,& \quad \text{if $x$ \( \geq 0\)}\\ \end{array} \right. $

asked Nov 10, 2012 by thanvigandhi_1

1 answer

For what value of \( \lambda \) is the function defined by \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} \lambda(x^2 - 2x) ,& \quad\text{ if $ x $ \(\leq 0\)}\\ 4x + 1,& \quad \text{if $x$ > 0}\\ \end{array} \right. $ Continuous at \(x = 0\)?

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Find the relationship between \(a\) and \(b\) so that the function \(f\) defined by $ f(x) = \left\{ \begin{array} {1 1} ax + 1 ,& \quad\text{ if $ x $ \(\leq 3\)}\\ bx + 3,& \quad \text{if $x$ > 3}\\ \end{array} \right. $ is continuous at \(x = 3\).

asked Nov 10, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} -2 ,& \quad\text{ if $ x $ \(\leq -1\)}\\ 2x,& \quad\text{ if $ -1 $ < x \(\leq1\)}\\ 2 ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by $ f(x) = \left\{ \begin{array} {1 1} 2x ,& \quad\text{ if $ x $ < 0}\\ 0,& \quad\text{if $ 0 $ \(\leq x\) \(\leq1\)}\\ 4x ,& \quad\text{ if $ x $ > 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the function $f$, where $f$ is defined by \[ f(x) = \left\{ \begin{array} {1 1} 3 ,& \quad\text{ if $ 0 $ \(\leq x\) \(\leq1\)}\\ 4,& \quad\text{if $ 1 $ < \(x\) < 3 }\\ 5 ,& \quad\text{ if $ 3 $ \(\leq x\) \(\leq10\)}\\ \end{array} \right. \]

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x . cos\; x \]

asked Nov 7, 2012 by thanvigandhi_1

0 answers

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x - cos\; x \]

asked Nov 7, 2012 by thanvigandhi_1

0 answers

Discuss the continuity of the following functions: \[ f ( x ) = sin\; x + cos\; x \]

asked Nov 7, 2012 by thanvigandhi_1

0 answers

Find all the points of discontinuity of $f$ defined by $f (x) = | x | – | x + 1 |.$

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Examine that sin | x | is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Show that the function defined by f (x) = | cos x | is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Show that the function defined by \( f (x) = cos (x^2) \) is a continuous function.

asked Nov 6, 2012 by thanvigandhi_1

1 answer

Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Show that the function defined by $ g (x) = x – [x] $ is discontinuous at all integral points. Here $ [x] $ denotes the greatest integer less than or equal to $x$.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Is the function defined by $ f (x) = x^2 - \sin\; x + 5 $ continuous at $ x =\pi $ ?

asked Nov 5, 2012 by thanvigandhi_1

1 answer

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