Questions asked by martin23239
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Let # f(x) # be the function # f(x) = 5^x  5^{x}. # Is # f(x) # even, odd, or neither ? Prove your result.

Suppose # s(x) # and # c(x) # are 2 functions where:
1) # s'(x) = c(x) # and # c'(x) = s(x); #
2) # s(0) = 0 # and # c(0) = 1. #
What can you say about the quantity:
# \qquad [ s(x) ]^2 + [ c(x) ]^2 # ?

Let # f(x) = x1. # 1) Verify that # f(x) # is neither even nor odd. 2) Can # f(x) # be written as the sum of an even function and an odd function ? a) If so, exhibit a solution. Are there more solutions ? b) If not, prove that it is impossible.

A linear chain is made of 20 identical links. Each link can be made in 7 different colors. How many # physically # different chains are there?

Is it possible for a finitelygenerated group to contain subgroups that are not finitelygenerated ? True or False. Prove your conclusion.

Which is bigger: # ( 1 + \sqrt{2} )^{ 1 + \sqrt{2} + 10^{9,000} } # or
# ( 1 + \sqrt{2} + 10^{9,000} )^{ 1 + \sqrt{2} } # ?
If your calculator could actually handle this  please put it away !! :)

Can you simplify # cos(x)cos(2x)cos(4x)cos(8x)cos(16x) ... cos(2^n x) # ?,

What can you say about the shape of the curve # f(x) = 7 cos( 1/3 x ) +
\sqrt{19} sin( 1/3 x ) # ?

#
( (x1)^4, (x1)^3, (x1)^2, (x1), 1 ),
( (x2)^4, (x2)^3, (x2)^2, (x2), 1 ),
( (x3)^4, (x3)^3, (x3)^2, (x3), 1 ),
( (x4)^4, (x4)^3, (x4)^2, (x4), 1 ),
( (x5)^4, (x5)^3, (x5)^2, (x5), 1 )
 = # ?

# ( 1, 1, 1, 1, 1, 1, 1), ( 2^6, 2^5, 2^4, 2^3, 2^2, 2, 1 ), ( 3^6, 3^5, 3^4, 3^3, 3^2, 3, 1 ), ( 4^6, 4^5, 4^4, 4^3, 4^2, 4, 1 ), ( 5^6, 5^5, 5^4, 5^3, 5^2, 5, 1 ), ( 6^6, 6^5, 6^4, 6^3, 6^2, 6, 1 ), ( 7^6, 7^5, 7^4, 7^3, 7^2, 7, 1 )  = #?

Can you determine the determinant below ? (Would have put it here, but system wouldn't take it  determinant just a tiny bit too big.) ...

In my profile, how do I get to a page that shows all my Notifications at once, if possible ? So far, I've found the drop down menu for this, but this doesn't allow for prolonged viewing of these, or working with them as a whole. Thanks !!

Are there polynomial functions whose graphs have:
11 points of inflection, but no max or min ?

Can you calculate #\qquad \qquad e^{ ( ( ln(2), 1, 1, 1 ), ( 0, ln(2), 1, 1), ( 0, 0, ln(2), 1 ), ( 0, 0, 0, ln(2) ) ) } \qquad # ?

Let #theta# be an angle where: #"1)" theta in "Quadrant III"# and #"2)" sin( theta ) =  15/17#.
What Quadrant does #12theta# belong to ?
No Calculators !!

Suppose #G # is a group where all nonidentity elements are of order 2. Is #G# abelian ?

# "Is there a group of order 48 in the set of" \ \ 3 xx 3 \ \ "matrices of integers ?" #
# "If so, can you exhibit one ? If not, prove its impossibility." #

Can you find the solutions of the equation:
# \qquad qquad \qquad x^2 + i x  i \ = \ 0 \ "?" #
Make sure to give your answers in standard complex form ( a + bi form).