Find a reasonable estimate of the limit
picture below

Hence, the limit of the function is:

1.5

Step-by-step explanation:

We have to find a reasonable estimate of limit of the given expression:

Since on putting the limit x=-1 we observe that the numerator and denominator both are equal to zero i.e we get a 0/0 form.Hence, we will apply L'hospitals rule to find the limit of the function.

We will firstly differentiate the numerator and denominator to obtain the limit.

On differentiating numerator we get:

and on differentiating denominator we obtain:

Hence, now we have to find the limit:

Hence, the limit of the function is:

1.5

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: