## When can you not use L Hopital’s?

L’**Hopital’s** rule only applies when the expression is indeterminate, i.e. 0/0 or (+/-infinity)/(+/-infinity). So stop applying the rule when **you** have a determinable form.

## Can L Hopital’s rule be applied to every limit?

Quick Overview. Recall that L’Hôpital’s **Rule** is used with indeterminate **limits** that have the form 00 or ∞∞. It doesn’t solve **all limits**. Sometimes, even repeated applications of the **rule** doesn’t help us find the **limit** value.

## What is meant by L Hospital rule?

: a theorem in calculus: if at a given point two functions have an infinite limit or zero as a limit and are both differentiable in a neighborhood of this point then the limit of the quotient of the functions is equal to the limit of the quotient of their derivatives provided that this limit exists.

## Why does L Hopital’s rule work?

L’**Hopital’s rule** is a way to figure out some limits that you can’t just calculate on their own. Specifically, if you’re trying to figure out a limit of a fraction that, if you just evaluated, would come out to zero divided by zero or infinity divided by infinity, you can sometimes use L’**Hopital’s rule**.

## What happens if you try to use L Hospital’s rule to find the limit?

**What happens if you try to use l’ Hospital’s Rule to find the limit**? **You** cannot **apply l’Hospital’s Rule** because the numerator equals zero for some value x = a **You** cannot **apply l’Hospital’s Rule** because the function is not differentiable.

## How do you pronounce L Hopital?

In American accent it will be pronounced as loh-pee-TAHL.

## What are the rules of limits?

The **limit** of a constant times a function is equal to the constant times the **limit** of the function. The **limit** of a product is equal to the product of the **limits**. The **limit** of a quotient is equal to the quotient of the **limits**. The **limit** of a constant function is equal to the constant.

## How do you prove l Hospital rule?

Proof of the Extended L’**Hospital’s Rule**:

Suppose L=limx→af(x)g(x), where both f and g go to ∞ (or −∞) as x→a. Also suppose that L is neither 0 nor infinite. Then L=limx→af(x)g(x)=limx→a1/g(x)1/f(x).

## Who invented L Hopital’s rule?

The rule is named after the 17th-century French mathematician **Guillaume de l’Hôpital**. Although the rule is often attributed to **L’Hôpital**, the theorem was first introduced to him in 1694 by the Swiss mathematician **Johann Bernoulli**.

## Is 0 divided by infinity indeterminate?

Thus as x gets close to a, < ^{f}^{(}^{x}^{)}/_{g}_{(}_{x}_{)} < f(x). Thus ^{f}^{(}^{x}^{)}/_{g}_{(}_{x}_{)} must also approach zero as x approaches a. If this is what you mean by “**dividing** zero by **infinity**” then it is not **indeterminate**, it is zero.

## How do you find limits?

**For example, follow the steps to find the limit:**

**Find**the LCD of the fractions on the top.- Distribute the numerators on the top.
- Add or subtract the numerators and then cancel terms.
- Use the rules for fractions to simplify further.
- Substitute the
**limit**value into this function and simplify.

## How do you know if a limit is indeterminate?

So, L’Hospital’s Rule tells us that **if** we have an **indeterminate** form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the **limit**.

## Why is 0 0 indeterminate?

When calculus books state that ** ^{}** is an

**indeterminate**form, they mean that there are functions f(x) and g(x) such that f(x) approaches 0 and g(x) approaches 0 as x approaches 0, and that one must evaluate the limit of [f(x)]

^{g}

^{(}

^{x}

^{)}as x approaches 0. In fact,

**= 1!**

^{}## Why is 0 times infinity indeterminate?

Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, **infinity** is the same thing as “1 over “, so “zero **times infinity**” is the same thing as “zero over zero”, which is an **indeterminate** form.