# What are the removable and non-removable discontinuities, if any, of #f(x)=2/(x+1)#?

There is a non-removable discontinuity when

If you want to know if the discontinuity is removable, you can just compute the limit and see if it exists :

Therefore, it is not removable.

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The function f(x) = 2/(x+1) has a removable discontinuity at x = -1. There are no non-removable discontinuities.

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The function ( f(x) = \frac{2}{x + 1} ) has a removable discontinuity at ( x = -1 ) because it results in a zero denominator, making the function undefined at that point. However, the function can be redefined at ( x = -1 ) by removing the singularity and defining ( f(-1) ) as a limit, resulting in a continuous function.

There are no non-removable discontinuities in the given function since it is defined for all real numbers except ( x = -1 ), where the function has a removable discontinuity. Therefore, there are no other points where the function is undefined or exhibits a non-removable discontinuity.

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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.

- What is the limit of # (x +sqrt((x^2)+(3x)))# as x goes to infinity?
- What's the limit of #(x^n-a^n)/(x-a)# as #x# approaches #a# , using the derivate number which is #f'(a)# ?
- What is # lim_(->-oo) f(x) = (xe^x)/x^2#?
- Evaluate the limit # lim_(n rarr 0) (lamda^n-mu^n)/n# ?
- What is the limit as #x# approaches #2# for #sin(x^2 - 3x + 2)/x^2 - 2#?

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