Is the answer is correct ??
lim ((x^10)-1)/(x-1)
x-->0
is the answer is 1 ???
Yes, the limit is 1. The problem for this function is when x>>1
thanks
if it is 1 how would be the answer ???
There is no problem with
lim ((x^10)-1)/(x-1)
x-->0
because you can substitute x=0 and get 1 as bobpursley said.
You probably meant
lim ((x^10 - 1)/(x-1)
x-->1
In that case (x^10 - 1) ÷ (x-1)
= x^9 + x^8 + ... + x + 1
and you have
lim x^9 + x^8 + ... + x + 1
x-->1
= 10
What do you mean by "how would be the answer"? The answer to this problem is 1.
To find the limit of a function as x approaches a specific value, you can either evaluate the function directly at that value or try to simplify it to a form that allows you to apply known limit rules.
In this case, let's simplify the given expression by factoring the numerator using the difference of squares formula. We have:
(x^10 - 1) = (x^5 + 1)(x^5 - 1)
Now, we can cancel out the common factor of (x - 1) in both the numerator and the denominator:
((x^10 - 1)/(x - 1)) = ((x^5 + 1)(x^5 - 1))/(x - 1)
Next, it is important to note that in the given problem, we are considering the limit as x approaches 0. Therefore, we need to remove any factor or term that would cause division by zero.
Since we canceled out a common factor of (x - 1), we have avoided division by zero at x = 1. So, we are left with:
((x^5 + 1)(x^5 - 1))/(x - 1)
Now, when we substitute x = 0 into the expression, we get:
((0^5 + 1)(0^5 - 1))/(0 - 1)
Simplifying further:
((1)(-1))/(-1) = -1
So, the correct answer is -1, not 1.