Recent questions in Continuity and Differentiability

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

Is the function defined by $f(x) = \left\{ \begin{array} {1 1} x + 5 ,& \quad\text{ if $ x $ $\leq 1$}\\ x - 5,& \quad \text{if $x$ > 1}\\ \end{array} \right.$ a continuous function?

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$ , where $f$ fined by $f(x) = \left\{ \begin{array} {1 1} x^{10} -1 ,& \quad\text{ if $ x $ $\leq 1$}\\ x^2,& \quad \text{if $x$ > 1}\\ \end{array} \right.$

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$ , where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} x^3-3 ,& \quad\text{ if $ x $ $\leq 2$}\\ x^2+1,& \quad \text{if $x$ > 2}\\ \end{array} \right.$

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$ , where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} x + 1,& \quad\text{ if $ x $ $\geq 1$}\\ x^2+1,& \quad \text{if $x$ < 1}\\ \end{array} \right.$

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$ , where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} \large \frac x { |\;x\;| },& \quad\text{ if $x$ < 0 }\\ -1 ,& \quad \text{if $x$ $ \geq 0$}\\ \end{array} \right.$

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$ , where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} \large \frac{ |\;x\;| }x,& \quad\text{ if x $\neq$ 0 }\\ 0 ,& \quad \text{if $x$ =0}\\ \end{array} \right.$

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Find all points of discontinuity of $f$ , where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} |\;x\;| + 3,& \quad\text{ if $ x $ $\leq -3$}\\ -2x ,& \quad \text{if $-3$ <x< 3}\\ 6x+2, & \quad\text{if $x$ $\geq 3$}\\ \end{array} \right.$

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Prove that the greatest integer function defined by $f(x) = [x], 0<x<3$ is not differentiable at $x = 1$ and $x = 2$

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Prove that the function $f$ given by $f(x) = | x - 1 |, x \in R\;$ is not differentiable at $\; x = 1$ .

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x in $\;\cos(\sqrt {x} \;)$

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x: $\;2\sqrt {cot (x^2)}$

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x: $cos \; x^3. sin^2 (x)^5$

asked Nov 8, 2012 by thanvigandhi_1

1 answer