I am thinking through a problem in a particular book's first section. It asks to complete the sentence: "The antiderivative of an odd function is always..."
And I think such an antiderivative is always even. Well the family of functions is a family of even functions so any particular explicit...
Can someone please help me with this one :) Let f :[-1,1] → ℝ be a continuous odd function. Show that for every ϵ >0 exist such real numbers a1,a3,...,a2n+1, so that ∣a1x+a3x3+...+a2n+1x2n+1 − f(x)∣ < ϵ
for every x ∈ [-1,1].
I was reading through my lial and hornsby trigonometry book and in section 3.2 I came across a new symbol. I looked across all of the greek alphabet and none of them are quite similar enough for me to come to the conclusion that they are the same letter I'm looking at. I don't expect it to be a...
How many numbers of 5 digits (1 to 9) can we form if 3 digits are odd numbers? No repetition and any order.
Number of odd numbers: 5
Number of even numbers: 4
5*4*3 * 4*3 = 720 combination possible with this order.
How many ways can we arrange the digits...
My proof: Let be n be an odd integer. From definition of odd, we have an integer a such that n = 2a + 1.
-n = -(2a + 1) = -2a - 1 // substitution
I am stuck here, how can I somehow remove the negative sign so that -n = 2a + 1.
I am having a hard time trying to wrap my head around this, I think it's because a bathtub landed on my head this morning, but can you help me understand this concept? I always assumed Tan was a negative identity, but I am at a loss for how to do the operations to arrive at an answer...
I'm trying to prove that xn+yn is divisible by (x+y), when x and y are integers, and n is a positive, odd integer. I previously proved that xn-yn was divisible by (x-y) with induction, so I figured a similar method would make sense here, but I end up going in circles... this is what I tried...
I have a couple of questions about the following problem which I have successfully solved in 2 different ways. My 2 solutions are in the attached image, I was unable to import the latex due to a forum latex length limit.
"The difference of the cubes of two consecutive odd positive integers...
I have a question related to odd ratio and statistical significant that I'd like to get your help. I have two groups A and B . Its odd ratio is 1.09. Its Z score is 57.215 and the P value is less than 0.001. Since it has a small P value then there is a statistical significant between...
given the digits 1,2,3,4,5 , you are required to form 5 digits numbers. If the digits may be used repeatedly , find the number of numbers formed in such a way that the even digits only occupy the odd positions?
the ans is 72... How to do this .
Suppose there is a group of permutation of a set with
Now this group has identity permutation( ) and inverse permutation( ) namely: and
But there is a theorem which says that:
"No matter how is written as a product of transpositions, the number of transpositions is even."
Please help me understand this format. I am not even sure what the problem is asking for. Is the y17 and y18 the 17th and 18th derivatives? I have never seen a problem written in this format so if you can help me understand the method I will hopefully be able to work the problems. See...