HOW many shapes 'do you see hare
1 answer:
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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.
Answer:
B) (5,-2)
Step-by-step explanation:
we have the equations:
We multiply the first equation by 3:
i will call this equation 1.
and we multiply the second equation by 2:
i will call this equation 2.
Now we subtract equation 2 from equation 1:
this is:
which gives:
and now that we know that we substitute this value in any of the original equations to find
using
we have:
so
the answer is which is option B.