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:
r1= -3
r2= (11/2)
Step-by-step explanation:
5-4r=17
-4r=17-5
-4r=12
r=13
and
5-4r=-17
-4r=-22
r= 11/2
Answer:
1st graph: D) Y = 2/3x
2nd graph: A) Y = 4/3x - 5
Step-by-step explanation:
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