When the accountants for lose-a-digit Computer, Inc. had finished preparing their annual budget, they presented the final figures to the president, I.M. Smart. “It looks like a good year,” he exclaimed. “The amount of the budget just happens to be the smallest number of cents (other than one cent) that is a perfect square, a perfect cube, and a perfect …

## Let z be a complex number z=x+iy x 0 and y0

Let z be a complex number z=x+iy x <>0 and y<>0 Prove: 1. If z+1/z is real then |z|=1 2. If |z|=1 then z+1/z is real

## Prove that: 1 + x/2 – (x^2)/8 < squareroot(1+x) 0

Prove that: 1 + x/2 – (x^2)/8 < squareroot(1+x) < 1 + x/2 if x>0 In particular, show that 1.375 < squareroot(2) < 1.5

## Here is what the problem asks for: Give an example of a polynomial function f of

Here is what the problem asks for: Give an example of a polynomial function f of degree 5 such that the only real roots of f(x) are -2,1,6 and f(2)=32. Show that your example works and leave f(x) in factored form.

## Given ( INTEGRAL ln square(x)dx, as x from n to n+1 ) = ( INTEGRAL ln square (n+x)dx, as x from 0 to 1 ) =

Given ( INTEGRAL ln square(x)dx, as x from n to n+1 ) = ( INTEGRAL ln square (n+x)dx, as x from 0 to 1 ) = ( INTEGRAL [[ln(n+x) – ln(x) + ln(n)]square] dx, as x from 0 to 1 ), (a) Verify that ( LIMIT (n/ln(n)) [INTEGRAL (ln square (x)dx) – (ln square (n))] as n approach to the …

## For a mapping %:A -> B, let == denote the kernel equivalence of %, and let *:A -> A== denote the natural mapping. Define $:A==

For a mapping %:A -> B, let == denote the kernel equivalence of %, and let *:A -> A== denote the natural mapping. Define $:A== -> B by $([a]) = %(a) for every equivalence class [a] in A==. 1. Show that $ is well defined and one-to-one, and that $ is onto if % is onto. Furthermore, show that % …

## If m =/ 0, then (m4)/m4 =

If m =/ 0, then (m4)/m4 = a)1 b)m2 c)m4 d)m12 e)m16

## Expand: (w+5)^4

Expand: (w+5)^4

## Show that z and iz have the same modulus.

Show that z and iz have the same modulus. How are the graphs of these two numbers related?

## Rewrite in the simplest form. State the GCF(greatest common factor) of numerator and denominator in each case.

Rewrite in the simplest form. State the GCF(greatest common factor) of numerator and denominator in each case. 1. 34/85 2. 123123/567567 Find 5/9+7/12 using three different denominators. Give your answers as mixed numbers in lowest terms. State the LCM (least common multiple)of the denominators.