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Differentiate \( (x^2-5x+8)(x^2+7x+9)\) in three ways mentioned : (i) by using product rule (ii) by expanding the product to obtain a single polynomial (iii) by logarithmic differentiation. Do they all give the same answer?
cbse
class12
modelpaper
2012
sec-b
q15
math
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asked
Jan 10, 2013
by
thanvigandhi_1
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Differentiate $ (x^2 - 5x + 8) (x^3 + 7x + 9 ) $ in three ways mentioned below:\begin{array}{1 1} (i)\;by\;using\;product\;rule & \;\\(ii)\;by\;expanding\;the\;product\;to\;obtain\;a\;single\;polynomial. & \;\\ (iii)\;by\;logarithmic\;differentiation. & \;\end{array} Do they all give the same answer?
cbse
class12
bookproblem
ch5
sec5
q17
p178
easy
sec-c
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
If \( u, v \: and \ w \) are function of \( x\) , then show that $ \large\frac{d}{dx}(u.v.w) = \frac{du}{dx}.v.w+u.\frac{dv}{dx}.w+u.v.\frac{dw}{dx}$In two ways first by repeated application or product rule, secondly by logatithmic differentiation.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
If $u,\: v$ and $w$ are functions of $x$, then show that $\large\frac{d}{dx} $$( u.v.w) =\large \frac{du}{dx} $$v.w + u . \large\frac{dv}{dx} $$. w + u.v. \large\frac{dw}{dx} $ in two ways - first by repeated application of product rule, second by logarithmic differentiation.
cbse
class12
bookproblem
ch5
sec5
q18
p179
medium
sec-b
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
Two firms X and Y decided to award prizes to their employees for three norms Obedience (O), Punctual (P), Quality of work (Q). Firm X decided to award Rs. 40000 for the three values to 2, 4, 7 employees respectively while Y decided to award Rs. 51000 to 4, 2, 8 employees respectively. If all the three prizes together amount to Rs. 8750, then (i) Represent the above situation by a matrix equation and form linear equation using matrix multiplication. (ii) Is it possible to solve the system of linear equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why?
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
Principal and staff of a school decided to award prizes to their students for three values Honesty (x) cleanliness (y), Punctuality (z) in two groups. Group A ( upto class VIII) and group B ( IX - XII). It is decided that Rs. 12000 for three values (x, y, z) for 3, 4, 5 students of Group A and Rs. 11040 for 5, 4, 3 student of group B respectively. If all the three prizes together amount to Rs. 2880, then (i) Represent above situation by a matrix equation and form linear equation using matrices. (ii) Is it possible to solve the system of linear equations so obtained using matrices? (iii) Which value you prefer to be rewarded most and why?
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 21, 2013
by
thanvigandhi_1
0
answers
Verify mean value theorem, if \( f(x)=x^3-5x^2-3x\) in the interval [a, b], where a = 1, b = 3. Find all \( c \in (1, 3)\) for which f' (c) = 0.
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Prove that \( tan^{-1} \bigg(\frac{\large 1}{\large 4} \bigg) + tan^{-1} \bigg( \frac{\large 2}{\large 9} \bigg ) = \frac{\large 1}{\large 2} cos^{-1} \bigg( \frac{3}{5} \bigg). \)
cbse
modelpaper
2012
sec-b
q12
ch2
medium
asked
Dec 26, 2012
by
thanvigandhi_1
1
answer
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