At a pumpkin patch, if Armando guesses the weight of his pumpkin within 0.3 pounds, he gets to take the pumpkin home for free. I
2 answers:
Answer: last option
Step-by-step explanation:
You know that the weight of his pumpkin 4.9 pounds and that, if he guesses its weight within 0.3 pounds, he will get the pumpkin for free.
Then, to find the minimum weight he can guess in order to get his pumpkin for free, it's necessary to write the expression:
Rewriting it:
To find the maximum weight he can guess in order to get his pumpkin for free, it's necessary to write the expression:
Rewriting it:
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Answer:
so the limits are 2 and 9
Step-by-step explanation:
We want to express as a integral. To do this, we have to identify
as a Riemann Sum that approximates the integral. (taking the limit makes the approximation equal to the value of the integral)
In general, to find a Riemann sum that approximates the integral of a function f over an interval [a,b] we can the interval in n subintervals of equal length and approximate the area (integral) with rectangles in each subinterval and them sum the areas. This is equal to
, where
is a selected point of the subinterval.
In particular, if we select the ending point of each subinterval as the , the Riemann sum is:
.
Now, let's identify this in .
The integrand is x² so this is our function f. When k=n, the summand should be because the last selected point is b. The last summand is
thus b=9 and b-a=7, then 9-a=7 which implies that a=2.
To verify our answer, note that if we substitute a=2, b=9 and f(x)=x² in the general Riemann Sum, we obtain the sum inside the limit as required.