13shudnt the ans for 8th 0 and not not defined
I think there is a lot of confusion on limits due to a post on forum
let us do the following problems...
Find the following
\\1) \lim_{x\rightarrow 1} (x^{n}) \\ \\2) \lim_{x\rightarrow 1^+} (x^{n}) \\ \\3) \lim_{x\rightarrow 1^-} (x^{n}) \\ \\4) \lim_{n\rightarrow \infty}\lim_{x\rightarrow 1^-} (x^{n}) \\ \\5) \lim_{n\rightarrow \infty}\lim_{x\rightarrow 1^+} (x^{n}) \\ \\6) \lim_{n\rightarrow \infty}\lim_{x\rightarrow 1} (x^{n}) \\ \\7) \lim_{n\rightarrow \infty, x\rightarrow 1^+} (x^{n}) \\ \\8) \lim_{n\rightarrow \infty, x\rightarrow 1^-} (x^{n}) \\ \\9) \lim_{n\rightarrow \infty, x\rightarrow 1} (x^{n}) \\ \\10) \lim_{x\rightarrow 1^+}\lim_{n\rightarrow \infty} (x^{n}) \\ \\11) \lim_{x\rightarrow 1^-}\lim_{n\rightarrow \infty} (x^{n}) \\ \\12) \lim_{x\rightarrow 1}\lim_{n\rightarrow \infty} (x^{n}) \\
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48 Answers
1yup deepansh u correct...
amrita
wats the diff between q. 5 and 7 ??
in ur limits//
nishantsah
ek case me there is one limit after another
ek me both limit together
amrita
??
1 min
o achha
samjhi
bad observation
:(
3i have one dbt sir
if a qn is asked like limx→af(x)=?
is it necessary to check LHL=RHL.pls reply
62@sankara It is necessary..
@ manipal.. but n is only an integer..
62\\1) \lim_{x\rightarrow 1} (x^{n}) \\ \\2) \lim_{x\rightarrow 1^+} (x^{n}) \\ \\3) \lim_{x\rightarrow 1^-} (x^{n}) \\ \\4) \lim_{n\rightarrow \infty}\lim_{x\rightarrow 1^-} (x^{n}) \\ \\5) \lim_{n\rightarrow \infty}\lim_{x\rightarrow 1^+} (x^{n}) \\ \\6) \lim_{n\rightarrow \infty}\lim_{x\rightarrow 1} (x^{n}) \\ \\7) \lim_{n\rightarrow \infty, x\rightarrow 1^+} (x^{n}) \\ \\8) \lim_{n\rightarrow \infty, x\rightarrow 1^-} (x^{n}) \\ \\9) \lim_{n\rightarrow \infty, x\rightarrow 1} (x^{n}) \\ \\10) \lim_{x\rightarrow 1^+}\lim_{n\rightarrow \infty} (x^{n}) \\ \\11) \lim_{x\rightarrow 1^-}\lim_{n\rightarrow \infty} (x^{n}) \\ \\12) \lim_{x\rightarrow 1}\lim_{n\rightarrow \infty} (x^{n}) \\
Q1) 1
Explanation: n is a constant.. It does not change.. hence it is obvious
Q2) 1
Explanation: n is a constant.. It does not change.. hence it is obvious
Q3) 1
Explanation: n is a constant.. It does not change.. hence it is obvious
Take an example: n=3 then do the same limit!
Q4) 1
n is constant till x has converged to 1-.. so before we take the 2nd limit of n-> infinity, the llimit has already converged to 1! hence the answer is 1
Q5) 1
n is constant till x has converged to 1-.. so before we take the 2nd limit of n-> infinity, the llimit has already converged to 1! hence the answer is 1
Q6) 1
n is constant till x has converged to 1-.. so before we take the 2nd limit of n-> infinity, the llimit has already converged to 1! hence the answer is 1
Q7) Not Defined
Basically it is from the definiton of every subsequence! That is not in syllabus. basically we can have a case when x->1 first and then n->infinity .. then in that case we will have 1 as the limit. In other case when x goes to infinity slower than n then the limit could be infinite or even numbers other than 1!
example will be x(n) = (1+1/n)
the limit will be e!
Q8) Not Defined
same explanation as 7
Q9) Not Defined
same explanatino as 7
Q10) infinite
here x is >1 .. and then n goes to infinity first.. so the limit will be infinite (I should have mentioned that x>1)
Q11) zero.. take the same reasoning as 10
Q12) Not Defined
Not defined because we dont know if initially x >1 or <1 or =1
In each of the 3 cases, we will get different answers!
basically 7,8,9 are not insyllabus..
I was trying to show that they are different tihngs from 10,11,12 and 4,5,6
Dont worry if you dont understand them
11SIR YA MEIN PAGAL HO GAYA HOON [17]
YA AAPKE ENSWERS WRONG HAIN[1]
1[12] yaha kuch samajh mein nahi aa raha hai....
e to power f(x)-1 into g(x) kahan lagta hai ???
11sir i am a dumb fool[17]
i thought my limits r good but u proved me wrong
so please kindly give the solutions to the suspected ones[1]
1[12] .... [1] that sum came out to be LIMIT ROCKZ really handy coz certain new things was known [1]
thnks bhaiya [1]
11sir ab aur intezaar nahin ho raha please tell the solutions also
106this wud be my solutions..
(1) lim(x→1)xn = 1 as LHL = 1n = RHL
(2) this is just RHL of abv Q
(3) this is just LHL of abv Q
(4) this means lim(n→∞)[lim(x→1)xn] first we evaluate lim(x→1)xn then the answr for that is evaluated for n→∞
so, it is lim(n→∞) 1 = 1
(5) This is lim(n→∞) of Q2. = lim(n→∞) 1 = 1
(6) this is lim(n→∞) of Q3 = 1lim(n→∞) 1 = 1
(7)(8)(9) this means simultaneously, x→1 and n→∞.. so undefined
106(10) it is basically lim(x→1+)x→∞ = infinity
(11) it is basically lim(x→1-)x→∞ = zero
(12) LHL ≠RHL hence limit is undefined.
13sry correctd myself while doing 1 i thot n tends to infinity
1take n=1, limx->1 x ...
from both sides it tends 1 ...
so 1... for q.no1.