Austin invested his saving in two investment found the amount he invested in fund A was 3 times as much as the amount he investe
1 answer:
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Answer:
f(x) = -2x + 7, when x > 1
f(x) = 4x + 1 when x ≤ 1
Step-by-step explanation:
The right side graph passe through points (1,5) and (2,3).
Hence, the equation of the line
⇒ (y - 5) = 2(1 - x)
⇒ y - 5 = 2 - 2x
⇒ y = -2x +7.......... (1)
Now, the left side graph passes through points (1,5) and (0,1)
Therefore, the equation of the graph will be
⇒ y - 5 = 4(x - 1)
⇒ y = 4x + 1 ........ (2)
Hence, the equation (1) gives the function in the right side of the given graph which does not include the point (1,5) and extends to the right from this point.
Therefore, f(x) = -2x + 7, when x > 1 (Answer)
Again, equation (2) gives the function in the left side of the given graph which includes the point (1,5) and extends to the left from this point.
Therefore, f(x) = 4x + 1 when x ≤ 1 (Answer)
Formula for Riemann Sum is:
interval is [1,3] so a = 1, b = 3
f(x) = 3x , sub into Riemann sum
Continue by simplifying using properties of summations.
Now you have an expression for the summation in terms of 'n'.
Next, take the limit as n-> infinity.
The limit of
goes to 0, therefore the limit of the summation is 12.
The area under the curve from [1,3] is equal to limit of summation which is 12.
interval is [1,3] so a = 1, b = 3
f(x) = 3x , sub into Riemann sum
Continue by simplifying using properties of summations.
Now you have an expression for the summation in terms of 'n'.
Next, take the limit as n-> infinity.
The limit of
The area under the curve from [1,3] is equal to limit of summation which is 12.