MathDB

(i) Solve the simultaneous inequalities,

x<\frac{1}{4x}

and

x<0

; i.e. find a single inequality equivalent to the two simultaneous inequalities. (ii) What is the greatest integer that satisfies both inequalities

4x+13 < 0

and

x^{2}+3x > 16

. (iii) Give a rational number between

11/24

and

6/13

. (iv) Express 100000 as a product of two integers neither of which is an integral multiple of 10. (v) Without the use of logarithm tables evaluate

\frac{1}{\log_{2}36}+\frac{1}{\log_{3}36}.

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