How do you find the limit of # (x^5 – 1)/(x – 1) # as x approaches 1?

Answer 1

I got that tends to #5#.

If you try directly using #1# you get the indeterminate form #0/0#. We can use de L'Hospital rule deriving top and bottom and then apply the limit as: #lim_(x->1)(x^5-1)/(x-1)=lim_(x->1)color(red)((5x^4-0)/(1-0))=#
as #x->1# we get:
#=lim_(x->1)(5x^4-0)/(1-0)=5/1=5#
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Answer 2

To find the limit of (x^5 – 1)/(x – 1) as x approaches 1, we can simplify the expression by factoring the numerator using the difference of squares formula. This gives us (x – 1)(x^4 + x^3 + x^2 + x + 1)/(x – 1). Since (x – 1) appears in both the numerator and denominator, we can cancel it out. This leaves us with the limit of (x^4 + x^3 + x^2 + x + 1) as x approaches 1. Plugging in x = 1 into the expression, we get 5. Therefore, the limit of (x^5 – 1)/(x – 1) as x approaches 1 is 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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