State whether each of the following limit forms is indeterminate. Where possible, state the limit. a 00 b c 0 d 0 e + f g h 0 i 0 j 0 k 0 l 1

**(a)**

**To State** wheather each of the following limit forms is intermidiate, where possible state the limit.

**Solution:**

**Given:**

Let

In this section, discovered that direct substitution can produce an intermediate form such as

Which tells noting about the limit, to find the limit one can factor and divide out like factors, as shown:

**Conclusion:** Hence,

**(b)**

**To State** whether each of the following limit form is intermediate, where possible, state the limit

**Solution:**

**Given:**

Take an example of the form.

Let

Apply L’s Hospital’s rule as shown,

**Conclusion:** Hence,

**(c)**

**To State** weather each of the following limit forms is intermediate. Where possible, state the limit

**Solution:** 0.

**Given:**

*x* is dry non-zero number so it is equal to 0.

Take an example:

Where *x* is any non-zero number so it is equal to 0.

**Conclusion:** Hence,

**(d)**

**To State** whether each of the following limit forms is indeterminate where possible, take the limit

**Solution:**

**Given:**

**Conclusion:** Hence,

**(e)**

**To State** whether each of the following limit form is indeterminate. Where possible, state the limit

**Solution:**

**Given:**

Take an example

Put the limit then get

**Conclusion:** Hence,

**(f) To State** weather each of the following limit factor indeterminate. Where possible, state the limit

**Solution:**

**Given:**

Put the limit in this equation.

**Conclusion:** Hence, this is the undefined value so this is the indeterminate form.

**(g)**

**To State** whether each of the following limit form is indeterminate, where possible state the limit.

**Solution:**

**Given:** ∞ · ∞

Take an example

Put the limit so get

**Conclusion:** Hence,

**(h)**

**To State** whether each if the following limit forms is indeterminate where possible state the limit

**Solution:**

**Given:**

Take an example.

Put the value of limit to get

So, this is undefined.

**Conclusion:** Hence,

**(i)**

**To State** whether each if the following limit forms is indeterminate where possible state the limit

**Solution:**

**Given:**

Take an example.

Put the value of limit to get

So, this is undefined.

**Conclusion:** Hence,

**(j)**

**To determine:** State whether each of the following limit form is indeterminate. Where possible state the limit

**Solution:**

**Given:**

Take an example.

Put the value of limit to get value equal to zero.

**Conclusion:** Hence,

**(k)**

**To State** whether each if the following limit forms is indeterminate where possible state the limit

**Solution:**

**Given:**

Take an example.

Put the value of limit to get

So, this is undefined.

**Conclusion:** Hence,

**(l)**

**To State** whether each if the following limit forms is indeterminate where possible state the limit

**Solution:**

**Given: **

Take an example.

Put the value of limit to get

So, this is undefined.

**Conclusion: **Hence,