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Recent questions in Continuity and Differentiability
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CBSE XII
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Math
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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. $
cbse
class12
bookproblem
ch5
sec1
q25
p160
sec-b
easy
math
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?
cbse
class12
bookproblem
ch5
sec1
q24
p160
sec-a
easy
math
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. $
cbse
class12
bookproblem
ch5
sec1
q23
p160
sec-b
easy
math
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 \(x = 0\)?
cbse
class12
bookproblem
ch5
sec1
q18
q18-1
p160
sec-a
easy
math
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 \(x = 3\).
cbse
class12
bookproblem
ch5
sec1
q17
p160
sec-b
easy
math
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. $
cbse
class12
bookproblem
ch5
sec1
q16
p160
sec-b
medium
math
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. $
cbse
class12
bookproblem
ch5
sec1
q15
p160
medium
sec-b
math
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. \]
cbse
class12
bookproblem
ch5
sec1
q14
p160
sec-b
easy
math
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?
cbse
class12
bookproblem
ch5
sec1
q13
p159
math
sec-b
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. $
cbse
class12
bookproblem
ch5
sec1
q12
p159
sec-b
medium
math
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. $
cbse
class12
bookproblem
ch5
sec1
q11
p159
sec-b
easy
math
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. $
cbse
class12
bookproblem
ch5
sec1
q10
p159
sec-b
easy
math
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. $
cbse
class12
bookproblem
ch5
sec1
q9
p159
sec-b
medium
math
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. $
cbse
class12
bookproblem
ch5
sec1
q8
p159
sec-b
easy
math
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. $
cbse
class12
bookproblem
ch5
sec1
q7
p159
sec-b
medium
math
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 $
cbse
class12
bookproblem
ch5
sec2
q10
p166
exercise5-2
sec-b
easy
math
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 $\; x = 1$.
cbse
class12
bookproblem
ch5
sec2
q9
p166
exercise5-2
sec-b
medium
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x in $\;\cos(\sqrt {x} \;) $
cbse
class12
bookproblem
ch5
sec2
q8
p166
exercise5-2
sec-a
easy
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x: $\;2\sqrt {cot (x^2)}$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q7
sec-b
easy
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x: $ cos \; x^3. sin^2 (x)^5 $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q6
sec-b
medium
math
asked
Nov 8, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to $x: \large \frac{ sin\; (ax + b) } { cos \;( cx + d)} $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-b
easy
q5
math
asked
Nov 8, 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} 2x + 3,& \quad\text{ if $ x $ \(\leq 2\)}\\ 2x - 3,& \quad \text{if $x$ > 1}\\ \end{array} \right. $
cbse
class12
bookproblem
ch5
sec1
q6
p159
sec-b
medium
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Is the function f defined by $f(x) = \left\{\begin{array}{l l} x, & \quad \text{if $x$ \( \leq \) 1}\\ 5, & \quad \text{if $x$ > 1}\\ \end{array} \right.$ continuous at $(x = 0)$? At $(x = 1)$? At $(x = 2)$?
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q5
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to $x$: $sec \;( tan (\sqrt x ) )$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-a
easy
q4
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the function with respect to x: $cos\;(sin x)$
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
sec-a
easy
q2
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions with respect to x: $ \; sin ( x^2 + 5 ) $
cbse
class12
bookproblem
ch5
sec2
exercise5-2
p166
q-1
sec-a
easy
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Discuss the continuity of the following functions: \[ f ( x ) = sin\; x . cos\; x \]
cbse
class12
bookproblem
ch5
sec1
q21c
p160
math
sec-b
asked
Nov 7, 2012
by
thanvigandhi_1
0
answers
Discuss the continuity of the following functions: \[ f ( x ) = sin\; x - cos\; x \]
cbse
class12
bookproblem
ch5
sec1
q21b
p160
math
sec-b
asked
Nov 7, 2012
by
thanvigandhi_1
0
answers
Discuss the continuity of the following functions: \[ f ( x ) = sin\; x + cos\; x \]
cbse
class12
bookproblem
ch5
sec1
q21a
p160
math
sec-b
asked
Nov 7, 2012
by
thanvigandhi_1
0
answers
Examine the following functions for continuity. $f(x) = | \;x - 5\;|$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-4
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity $\; f(x) = \large \frac {x^2 - 25} {x + 5}$$, x\:\neq\: -5$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-3
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-2
math
asked
Nov 7, 2012
by
thanvigandhi_1
1
answer
Examine the following functions for continuity. $f(x) = x-5$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q3
q3-1
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Find all the points of discontinuity of $f$ defined by $f (x) = | x | – | x + 1 |.$
cbse
class12
bookproblem
ch5
sec1
q34
p160
sec-c
medium
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Examine that sin | x | is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q33
p160
sec-b
medium
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Show that the function defined by f (x) = | cos x | is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q32
p160
sec-b
medium
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Show that the function defined by \( f (x) = cos (x^2) \) is a continuous function.
cbse
class12
bookproblem
ch5
sec1
q31
p160
sec-b
easy
math
asked
Nov 6, 2012
by
thanvigandhi_1
1
answer
Discuss the continuity of the cosine, cosecant, secant and cotangent functions.
cbse
class12
bookproblem
ch5
sec1
q22
p160
sec-c
difficult
math
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 $x$.
cbse
class12
bookproblem
ch5
sec1
q19
p160
sec-b
easy
math
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 $ ?
cbse
class12
bookproblem
ch5
sec1
q20
p160
sec-b
easy
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Prove that the function \( f (x) = x^n \) is continuous at \( x = n \), where n is a positive integer.
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
sec-a
easy
q4
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Examine the continuity of the function $f (x) = 2x^2 - 1$ at $x = 3$
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
q2
sec-a
easy
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Prove that the function $f (x) = 5x-3$ is continuous at $x=0$, $x=-3$ and $x=5$.
cbse
class12
bookproblem
ch5
sec1
exercise5-1
p159
q1
sec-a
easy
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
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