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Thanks!
^^just edited my earlier post. It is for the first one.
Wow! A lot of discussions on hmms.. in this post.
Now, the answer in the book says that the answer for question (1) is 1/2.
Is it right or there is a printing mistake?
I am trying to solve questions like:
1.
How do I solve them?
for the first one, i get upto lim 1/n+2. Then what should I do?
Well, to identify and prove a geometric progression the following can be used:
If
t2/t1=t3/t2=t4/t3=.....=tn/t(n-1)=r (and 'r' also represents common ratio)
then the sequence is a GP.
Here,
1/2^4 divided by1/2 is equal to 1/2^7 divided by 1/2^4.
Thus, you can show that it is a gp
I have read all basics of trignometry and I have a question:
Find
I have read all the questions related to these on mathsisfun.com but all the questions there are like sin 330 is given and a related acute angle's value is given.
But how do I convert this into an acute angle?
Are you asking about proof by Mathematical Induction?
^^Thanks. Now I understood the concept.
(1)
Notice that [x] ≤ x < [x]+1 for all x∈ R.
x ∈ R-Z
=> 0 < x-[x] < 1
=> 1/(x-[x]) > 1
=> f(x) = 1/sqrt(x-[x]) = sqrt(1/(x-[x])) > 1
Thanks. But what do you mean when you say that since x∈R-Z so the equation 0<x-[x]<1.
And thanks very much for the second question. I realised what I was doing wrong.
^^Thanks.
I have done it as you said.
x-[x] ≤0
=> x≤[x]
That is only possible when x is an element of Z(Integers)
=> Domain is (R-Z) [R is the set of real nos. and Z is that of integers].
Now for Range, what should I do?
I have been able to find the domain and ranges of questions but this one is not coming:
(1)
Also,
(2) This modulus function question, I am not able to understand how to get values for the conditions:
If f(x) be defined on
and is given byand g(x) = f(|x|) + |f(x)|. Find g(x). Here | | means Modulus.
Thanks.
Lets say, I begin answering by:
And, in some books I see that, suddenly out of the blues, a person adds
to and makes it
Now, I have understood that after reading the same question for the past 5 days.
But your method seems to be faster.
Thanks
And if
I know that a principal solution of a trignometric equation is 2 values lying between
That means that the fx is undefined for denominator=0 because anything/0=undefined
One last thing please,
Can you explain how to solve
|x-2|/x-2 ≥ 0
My ans is:x ≥2
But book's ans is: x>2
Thanks. Finally I understood something...
^^Thanks.
In the book, the answer given is
soln. set of the inequation is (-infinity,-2) union (-1/2, +infinity).
But, you have given x<2 which would mean (-infinity, 2)
@bob bundy
I have two for you:
1. |x-1|/x+2<1
2. |x-1|+|x-2| ≥4
^^ thanks. But how to do a little faster without a graph? I am seeing books which use zeroes of the linear equations given in numerator and denominator enclosed in the mods and then proceed.
Thanks...
One thing more,
Can you show me a detailed procedure on how to solve inequations with the moduluses like | x-1 |
My question,
1. But how to proceed ahead? Please explain me step-by-step.
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2. When you reach the end, you get two values(here, fractions), say c and d. Then how do you decide whether:
Q. Show that for any sets A and B, A = (A ∩ B) ∪ (A B).
Please show me by the method of "let x∈A..."
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