Can someone answer these questions to me understand? and you! will mark as

QUESTION 1  

If a function is continuous at , then  

Let us find the limit first,  

As , , and  

Let us now find the functional value at  

Since  

, the function is continuous at .  

QUESTION 2  

The correct answer is table 2. See attachment.

In this table the values of x approaches zero from both sides.

This can help us determine if the one sided limits are approaching the same value.

As we are getting closer and closer to zero from both sides, the function is approaching 2.

The values are also very close to zero unlike those in table 4.

The correct answer is B

QUESTION 3

We want to evaluate;

using the properties of limits.

A direct evaluation gives .

This indeterminate form suggests that, we simplify the function first.

We factor to obtain,

We cancel common factors to get,

The correct answer is D

QUESTION 4

We can see from the table that as x approaches from both sides, the function approaches

Hence the limit is .

See attachment

The correct answer is option A

the correct answer is the last option