Assume postage for sending a first-class letter in the United ...

Question

Assume postage for sending a first-class letter in the United States is $0.47 for the first ounce (up to and including 1 oz) plus $0.21 for each additional ounce (up to and including each additional ounce).

b. Evaluate lim w→2.3 f(w).

b. Evaluate lim w→2.3 f(w).

Accepted Answer

Welcome back, everyone. A local bakery sells sourdough bread for $3 for the first pound and $0.75 for each additional pound. Determined limit of F of WSW approaches 1.9, where FFW is the cost for selling sourdough bread weighing W pounds, and we are given four answer choices A $3.75 B $4.75 C $5.75 and D $3.00. So essentially, what we're going to do is basically understand that we are trying to identify the limit as W approaches 1.9 of a function F of W, but this function is not given, so first of all, Let's define that function. If we look at the limit, well, W approaches 1.9, right? So essentially we're looking at a function where we have 1 pound, but. Plus An additional pound, right? So essentially we're going to round to the nearest whole pound because we have a fixed price of $0.75 for each additional pound. So we have 1 pound initially plus 1 additional pound. And we can define FFW as follows. First of all, we are paying $3 for the first pound. And then we are paying $0.75 for each additional pound, right? So we have to multiply that by W minus 1. The reason why we're subtracting one is simply because, well, W represents the total number of pounds of the bread that we are buying, right? So for the first pound we're only paying $3 if we substitute one, the second term disappears. If we substitute two. Pounds while we're getting $0.5 additionally. So we have our function, and now what we want to do is basically substitute it into the limit. So we get limit as W approaches 1.9 of F of W, which is 3 + 0.75 multiplied by W minus 1. And now we can see that this is a linear function, so we can evaluate our limit directly by substituting the value of W. And also we have to say that W is approximately equal to 2, right? We have to round to the nearest whole pound based on the context of the problem. So we're going to get 3 + 0.75 multiplied by 2 minus 1. And this essentially gives us 3.75. 2 minus 1 gives us 11 multiplied by 0.75 gives us 0.75, and then we're adding 3 to end up with the final answer. Which corresponds to the answer choice A. Thank you for watching.