Question

Use the following expressions for left and right sums left sum = f(t0)Δt + f(t1)Δt +...

Use the following expressions for left and right sums

left sum = f(t0)Δt + f(t1)Δt + f(t2)Δt +    + f(tn − 1)Δt
right sum = f(t1)Δt + f(t2)Δt + f(t3)Δt +    + f(tn)Δt

and the following table.

t 0 4 8 12 16

f(t)

 25 22 20 18 15

(a) If n = 4, what is Δt?

Δt =



What are

t0, t1, t2, t3, t4?

t0 =
t1 =
t2 =
t3 =
t4 =



What are

f(t0), f(t1), f(t2), f(t3), f(t4)?

f(t0) =
f(t1) =
f(t2) =
f(t3) =
f(t4) =



(b) Find the left and right sums using n = 4.

left sum
right sum    



(c) If n = 2, what is Δt?

Δt =



What are

t0, t1, t2?

t0 =
t1 =
t2 =



What are

f(t0), f(t1), f(t2)?

f(t0) =
f(t1) =
f(t2) =



(d) Find the left and right sums using n = 2.

left sum
right sum    
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