- #1
shawshank
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limit of x --> 1
(x^1000 - 1 ) / (x-1)
(x^1000 - 1 ) / (x-1)
The Rule for Finding Limits of Difference of Powers: (a^n - b^n)
- Thread starter shawshank
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In summary, the conversation was about finding the limit of x as it approaches 1 in the equation (x^1000 - 1) / (x-1). Suggestions were given to use the formula (a^n - b^n) = (a-b)(a^(n-1) + a^(n-2)b + ... + b^(n-1)) and to look up l'Hôpital's Rule. The final answer was determined to be 1000.
- #2
sutupidmath
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what have you done so far? show your work before someone here gives you any hints!
- #3
shawshank
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lim of x ---> 1
(x^1000)(x+1)/(x^2-1)
hahah, lol just kidding.
seriously, have no clue where to start.
(x^1000)(x+1)/(x^2-1)
hahah, lol just kidding.
seriously, have no clue where to start.
- #4
sutupidmath
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ok, then let's do this before i get out of here:
well i am going to try to give u a hint
[tex] a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^{2}+a^{n-4}b^{3}+...+a^{2}b^{n-3}+ab^{n-2}+b^{n-1})[/tex], in your problem a=x, b=1 , and n=1000, also remember that 1=1^1000, or any other real power.
i hope this will do u any good!
well i am going to try to give u a hint
[tex] a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^{2}+a^{n-4}b^{3}+...+a^{2}b^{n-3}+ab^{n-2}+b^{n-1})[/tex], in your problem a=x, b=1 , and n=1000, also remember that 1=1^1000, or any other real power.
i hope this will do u any good!
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- #5
shawshank
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thanks i got it, it's 1000. What is the rule called the (a^n - b^n).
- #6
tiny-tim
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l'Hôpital's Rule
Or you could look up "l'Hôpital's Rule" (try wikipedia or any elementary textbook on calculus).
But I agree, sutupidmath's method is the easy and obvious one in this case (and yes it is 1000)!
Or you could look up "l'Hôpital's Rule" (try wikipedia or any elementary textbook on calculus).
But I agree, sutupidmath's method is the easy and obvious one in this case (and yes it is 1000)!
- #7
sutupidmath
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shawshank said:
i am not sure how do u call it in english, but it is merely the diference of powers i guess!
FAQ: The Rule for Finding Limits of Difference of Powers: (a^n - b^n)
What is a limit?
A limit is a fundamental concept in calculus that represents the value that a function approaches as its input (usually denoted as x) gets closer and closer to a specific value.
How do you solve a limit?
To solve a limit, you can use algebraic manipulation, substitution, or special limit rules such as the product, quotient, or power rules. You can also use graphing or numerical methods to approximate the limit.
What does it mean for a limit to exist?
A limit exists if the function has a well-defined value at the point it is approaching. In other words, the left and right limits must approach the same value for the limit to exist.
What is the difference between a left and right limit?
A left limit, also known as a one-sided limit, approaches the specified value from the left side of the function. A right limit approaches the value from the right side.
Can a limit have a different value than the function at the specified point?
Yes, a limit can have a different value than the function at the specified point. This occurs when the function is either undefined or has a discontinuity at that point.