Lim ₓ→∞ (x+4/x-1)∧x+4​

It looks like the limit you want to find is

One way to compute this limit relies only on the definition of the constant e and some basic properties of limits. In particular,

The idea is to recast the given limit to make it resemble this definition. The definition contains a fraction with x as its denominator. If we expand the fraction in the given limand, we have a denominator of x - 1. So we rewrite everything in terms of x - 1 :

Now in the first term of this product, we substitute y = (x - 1)/5 :

Then use a property of exponentiation to write this as

In terms of end behavior, (x - 1)/5 and x behave the same way because they both approach ∞ at a proportional rate, so we can essentially y with x. Then by applying some limit properties, we have

By definition, the first limit is e and the second limit is 1, so that

You can also use L'Hopital's rule to compute it. Evaluating the limit "directly" at infinity results in the indeterminate form .

Rewrite

so that

and now evaluating "directly" at infinity gives the indeterminate form 0/0, making the limit ready for L'Hopital's rule.

We have

and so

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)