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Recent questions tagged sec2
Questions
Let $A=R-\{3\}$ and $B=R-\{1\}$. Consider the function $ f:A \to B$ defined by $f(x)=\large\frac {x-2}{ x-3}$. Is $f$ one-one and onto?
cbse
class12
bookproblem
ch1
sec2
q10
p11
medium
sec-b
math
asked
Nov 9, 2012
by
vaishali.a
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
Let \(A\) and \(B\)be sets. Show that\(f : A × B \to\; B×A\)such that \( f(a,b)\,=\,(b,a)\) is bijective function
cbse
class12
bookproblem
ch1
sec2
q8
p11
medium
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.(i) \(f : R\; \to R\; defined \; by \; f(x)\; =\; 3-4x\)
cbse
class12
bookproblem
ch1
sec2
q7
q7-1
p11
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
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
Let \(A=\{1,2,3\},\; B = \{4,5,6,7\}\) and let \(f = \{(1,4),(2,5),(3,6)\}\)be a function from \(A\) to \(B\). Show that \(f\) is one-one.
cbse
class12
bookproblem
ch1
sec2
q6
p11
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the Signum Function \(f : R \to R\), given by \[ f(x) = \left\{ \begin{array}{l l} 1, & if \; x \; > 0 \\ 0, & if\; x\;= 0 \text{ is neither one-one nor onto } \\ -1, & if\; x \;< 0 \end{array} \right. \]
cbse
class12
bookproblem
ch1
sec2
q5
p11
easy
sec-a
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the Modulus Function \(f : R \to R\), given by \( f(x) = |\;x\;|\), is neither one-one nor onto, where\( |\;x\;|\; is\; x\), if \(x\) is positive or \(0\) and \(|\;x\;|\; is\; \) \(-\)\(x\), if \( x\) is negative.
cbse
class12
bookproblem
ch1
sec2
q4
p11
sec-a
medium
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Prove that the Greatest Integer Function \(f : R \to R\), given by \(f (x) = [x]\), is neither one-one nor onto, where \([x]\) denotes the greatest integer less than or equal to \(x\).
cbse
class12
bookproblem
ch1
sec2
q3
p10
easy
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Check the injectivity and surjectivity of the function: $f : N\to N\; given\; by\; f(x)\; = x^2 $
cbse
class12
bookproblem
ch1
sec2
q2
q2-1
p10
easy
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
1
answer
Show that the function \(f : R_* \rightarrow R_* \) defined by \( f(x) = (\frac{1} {x})\) is one-one and onto, where \(R_* \) is the set of all non-zero real numbers. Is the result true, if the domain \(R_* \) is replaced by \(N\) with co-domain being same as \(R_*\)?
cbse
class12
bookproblem
ch1
sec2
q1
p10
easy
sec-b
math
asked
Nov 8, 2012
by
vaishali.a
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
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