Use the expressions for left and right sums and the table below.

right-hand sum = summation (n above and i =1 on the bottom) f(ti) * change in t = f(t1) * change in t + f(t2) * change in t + .... + f (tn) * change in t
left-hand sum = summation (n above and i = 0 on the bottom) f(ti) * change in t = f (t0) * change in t + f (t1) * change in t + ... = f (tn - 1) * change in t.

Table: t 0 4 8 12 16
f (t) 26 24 23 21 18
If the table messed up, the points are (0, 26), (4, 24) , (8, 23) , (12, 21), (16, 18)

a.) If n = 4, what is change in t? What are t0, t1, t2, t3, t4? What are f (t0), f (t1), f (t2), f (t3), f(t4)?
t0= f (t0) =
t1 = f (t1) =
t2 = f (t2) =
t3 = f (t3) =
t4 = f (t4) =

b.) Find the left and right sums using n = 4.
Left sum =
Right sum =

c.) If n = 2, what is change in t? What are t0, t1, t2? What are f (t0), f (t1), f(t2)?
t0 = f (t0) =
t1 = f (t1) =
t2 = f (t2) =

d.) Find the left and right sums using n = 2
Left sum =
Right sum =

Please show work and explain. I have a couple more problems like this and I don't know how to do them!

To solve this problem, we will follow the given expressions for left and right sums and use the table of values provided.

a) If n = 4, the number of intervals is 4. Since we have 5 data points in the table, each interval will have a width of: change in t = (16 - 0)/4 = 4.

Now, we can determine the values for t0, t1, t2, t3, and t4 using the interval width:

t0 = 0 + 0*4 = 0
t1 = 0 + 1*4 = 4
t2 = 0 + 2*4 = 8
t3 = 0 + 3*4 = 12
t4 = 0 + 4*4 = 16

Using these values, we can find the corresponding function values:

f(t0) = 26
f(t1) = 24
f(t2) = 23
f(t3) = 21
f(t4) = 18

b) To find the left and right sums using n = 4, we substitute the values into the respective expressions:

Left sum = f(t0) * change in t + f(t1) * change in t + f(t2) * change in t + f(t3) * change in t = 26 * 4 + 24 * 4 + 23 * 4 + 21 * 4
Right sum = f(t1) * change in t + f(t2) * change in t + f(t3) * change in t + f(t4) * change in t = 24 * 4 + 23 * 4 + 21 * 4 + 18 * 4

Now you can simply calculate both the left and right sums.

c) If n = 2, the number of intervals is 2. The interval width can be calculated as: change in t = (16 - 0)/2 = 8.

Using this interval width, we can determine the values for t0, t1, and t2:

t0 = 0 + 0*8 = 0
t1 = 0 + 1*8 = 8
t2 = 0 + 2*8 = 16

Now, we can find the corresponding function values:

f(t0) = 26
f(t1) = 24
f(t2) = 18

d) To find the left and right sums using n = 2, we substitute the values:

Left sum = f(t0) * change in t + f(t1) * change in t = 26 * 8 + 24 * 8
Right sum = f(t1) * change in t + f(t2) * change in t = 24 * 8 + 18 * 8

Calculate both the left and right sums using these values.

Remember, change in t is determined by dividing the total interval width by the number of intervals. The values of t0, t1, t2, etc., are found by multiplying the interval number by the change in t and adding it to the starting value. The values of f(t0), f(t1), f(t2), etc., are obtained from the table of values provided. Finally, the left and right sums are calculated by multiplying each f(ti) value with the change in t and summing them up according to the respective formulas.