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Recent questions tagged q8

Differentiate the following w.r.t. $x :$$ log ( log \: x ), x > 1 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

A merchant plans to sell two types of personal computers, a desktop model and a portable model that will cost Rs 25000 and Rs 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant would stock to get maximum profit if he does not want to invest more than Rs 70 lakhs and if his profit on the desktop model is Rs 4500 and on portable model is Rs 5000.

asked Nov 16, 2012 by fingeazy

1 answer

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table below. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? \[\] $\begin{matrix} \text{kg per bag:}& \text{Brand P} &\text{Brand Q} \\ \text {Nitrogen} &3 & 3.5\\ \text {Phosphoric Acid}& 1 & 2\\ \text {Potash}&3 &1.5 \\ \text {Chlorine}& 1.5 & 2 \end{matrix}$

asked Nov 16, 2012 by fingeazy

1 answer

Consider \( f:R_+ \to [4,\infty)\)given by \(f(x)=x^2 +4\). Show that \(f\) is invertible with the inverse \(f^{-1}\)of \(f\) given by \(f^{-1}(y) = \sqrt {y-4}\),where $R_+$ is the set of all non-negative real numbers.

asked Nov 14, 2012 by vaishali.a

1 answer

Find $ \frac {dy}{dx} $ in the following: $ \sin^2x +\cos^2y = 1 $

asked Nov 11, 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

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

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

asked Nov 8, 2012 by vaishali.a

1 answer

Show that the relation \(R\) in the set \(A= \{1,2,3,4,5\} \)given by \(R = \{(a, b) : |a – b| \,is\, even \} \), is an equivalence relation. Show that all the elements of \(\{1, 3, 5\} \) are related to each other and all the elements of \(\{2, 4\}\) are related to each other. But no element of \( \{1, 3, 5 \} \) is related to any element of \(\{2, 4\}\).

asked Nov 7, 2012 by vaishali.a

1 answer

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