Step-by-step explanation:
A left Riemann sum approximates a definite integral as:

Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
Answer:
B: 6
Step-by-step explanation:
Find the mean:
5+8+4+7= 24
24/4=6
Answer:
2
Step-by-step explanation:
6 plus 7 equals 13
9 plus 9 equals18
18 subtract 6 equals 13
13 subtract 12 equals 1