# Can all limits questions be solved algebraically?

• lionely
In summary, not all limits can be solved algebraically. Indeterminate forms such as 0/0 or infinity/infinity cannot be solved using direct substitution. Indeterminate forms in limits refer to situations where the value of the limit cannot be determined using direct substitution. To solve limits algebraically, limit laws and algebraic manipulation can be used to simplify the expression until a direct substitution can be made. However, if the limit involves an indeterminate form, additional techniques such as L'Hôpital's rule may be necessary. There are also limits that cannot be solved algebraically or numerically, known as non-computable limits. These require advanced mathematical techniques to determine their value. Limits can also be solved using a graph, particularly for
lionely
$$\lim_{n\rightarrow 0} {\frac{√(x+4) - 2}{x}}$$The answer is supposed to be 1/4. When I work it this way:

(√(x+4) - 2]/x )(√(x+4) + 2]/√(x+4) +2]

and then put in 0 I get 0..

Oh sorry I A FLIPPING IDIOT! ..... I AM SO STUPID my gosh, all I had to do was divide it by x... and I would 1 and 4 as the numerator and denominator respectively.

lionely said:
(√(x+4) - 2]/x )(√(x+4) + 2]/√(x+4) +2]
Bracketing is a bit off. I guess you mean (√(x+4) - 2]/x )(√(x+4) + 2)/(√(x+4) +2)
and then put in 0 I get 0..

## 1. Can all limits be solved algebraically?

No, not all limits can be solved algebraically. Some limits may involve indeterminate forms such as 0/0 or infinity/infinity, which cannot be solved algebraically.

## 2. What are indeterminate forms in limits?

Indeterminate forms in limits refer to situations where the value of the limit cannot be determined using direct substitution. These include forms such as 0/0, infinity/infinity, and infinity - infinity.

## 3. How do you solve limits algebraically?

Limits can be solved algebraically by using limit laws and algebraic manipulation to simplify the expression until a direct substitution can be made. If the limit involves an indeterminate form, additional techniques such as L'Hôpital's rule may be used.

## 4. Are there any limits that cannot be solved algebraically or numerically?

Yes, there are limits that cannot be solved algebraically or numerically. These are known as non-computable limits and require advanced mathematical techniques to determine their value.

## 5. Can you solve limits using a graph instead of algebraically?

Yes, limits can also be solved using a graph, particularly for limits involving piecewise functions or discontinuous functions. The graph can help to visualize the behavior of the function and determine the limit at a given point.

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