Define the sequence of functions f_k(x) = √(x²+1/k) for k ∈ ℕ. For both spaces each f_k(x) is always an element but the sequences limit f(x) = |x| is not. Therefore both can’t be Banach spaces right? My problem is that the role of the norm is confusing me. Last time I talked to a friend about it, that was his explanation of why (C¹[0,1], ||•||c⁰) is not a Banach space but that only confused me more than solve the problem. submitted by /u/MathematicalHuman314 [visit reddit] [comments ..read more

Question :- 38 fruits, apples, oranges, plums and guavas, are distributed among 4 people A, B, C and D. Each one gets a minimum of one fruits of each type and a maximum of four fruits of each type. There are 12 apples. There are two females, each of whom has the highest number of fruits. D, who has 3 plums, has 5 fruits less than the person who has the highest number of fruits. A has 4 apples and 4 plums and does not have the lowest number of fruits. B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. None of the friends has an eq ..read more

Hi, I am currently trying to do my math homework but can't complete this question. Factorise fully: 25x + 40 + 15qx + 24q I am unsure how to work it out. I can do more simple multi-variable factorising like x^2 + 4xy - 5y^2 but this one confuses my brain lol. Any help would be appreciated :) submitted by /u/Burdog_YT [visit reddit] [comments ..read more

Hi, i have this inequality y^2−6y+5>0 and i've found the two solutions 1 and 5 so i thought that the final solutions was y > 1 and y>5, but the book says that the solutions are y<1 and y>5, but why y<1 and not y>1? submitted by /u/Walmiltur [visit reddit] [comments ..read more

Can anyone explain me this please why it's negative? It is in the second quadrant! The first and second quadrant is positive and third and fourth is negative shouldn't it be like that? https://ibb.co/jzkkjL1 where is the sin and cos negative or positive? submitted by /u/Lifelegdy [visit reddit] [comments ..read more

So, I recently learned imaginary numbers, and the idea of a parabola which does not meet the x-axis in two dimensions, but does in three, was explained to me. It got me thinking: is there a set of numbers like this for every dimension? Can a graph which does not intercept the x-axis (or any point) in the third dimension possibly intercept it at the fourth? Thinking past 2D is all very new to me, so this might be a dumb question. Thanks in advance to anyone who answers (: submitted by /u/Lezley_ [visit reddit] [comments ..read more

I am just starting with propositional logic, but I don't understand if we care about the statements being factually correct ~ by factually, i mean if they are correct in real life or not Like, let's say that we have: p: The earth is made of cheese q: Humans are mortal We created the compound statement using the logical operator "AND". What we have is: "p and q" ~ basically "The earth is made of cheese and humans are mortal". Now, if we wanted to find out whether this compound statement is true or not, we would have to look at the atomic statements: p, q But, we already know that "the earth is ..read more

Hello, first of all, sorry foy my bad English. I was studying implicit derivative and everything went great until i found this problem: x^2= x-y/x+y I thought that is was easier if I rewrite the expression as x^2(x+y)=x-y, so the final expression would be x^3 +yx^2=x-y. I did it and everything was ok until i look at the answer that is in the book and its completely different, then i went to Symbolab and in fact the answer that symbolab gave me from that problem was the same that i got, but when i put x^2=x-y/x+y in symbolab it gave me another answer that is the same that it is in the book. So ..read more

X0 -1 -3 2 X1 = 0 + s 1 + t -4 X2 1 6 -4 -3 1 6 1 0 -2 2 -4 -4 0 1 0 After REF How do I turn it to A = [2, 0, 1] so that I can use it to multiply with -1 0 1 to get -1 submitted by /u/1g0tquestions [visit reddit] [comments ..read more

Problem: An empty lot with a width of 51.5 feet and a length of 30 feet has been approved for the development of a new playground. You are able to increase the length of playground by clearing some debris behind the lot. Write an expression to represent the total area of the playground. Be sure your expression accounts for the unknown amount of space you will gain by clearing debris. Sketch a design for your playground. Split the lot into four sections using one vertical line and one horizontal line. Write an expression to represent the area or each section. Make a model of your playground an ..read more