Calculate the limit of the fraction (f(x)-f(1))/(x-1) if f(x)=x^300+x+1, x-->1

### 2 Answers | Add Yours

We notice that if we'll calculate the limit of the given ratio, we'll calculate the first derivative of the given function, for x = 1.

lim (f(x)-f(1))/(x-1) = f'(1)

For this reason, we'll calculate first the derivative of the function:

f'(x) = 300x + 1

Now, to evaluate f'(1), we'll substitute x by 1 in the expression of derivative:

f'(1) = 300*1 + 1

f'(1) = 301

So, it is no need to struggle calculating the limit of the ratio, when we can do an easier way:

**lim [(f(x)-f(1))/(x-1)] = 301 for x-> 1**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes