smc-756-10-Log/Exponential

Calculus, MET2 2008 VCAA 3 MC

The average value of the function with rule `f(x) = log_e (3x + 1)` over the interval `[0, 2]` is

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`D`

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MARKER’S COMMENT: Almost a quarter of students found the average rate of change!

`y_text(avg)`	`= 1/(2 – 0) int_0^2 log_e (3x + 1)\ dx`
	`= (7 log_e(7) – 6)/6`

`=> D`

The average value of the function `f(x) = e^(2x) cos (3x)` for `0 <= x <= pi` is closest to

A. `– 82.5`

B. `26.3`

C. `– 26.3`

D. `– 274.7`

E. `pi`

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`C`

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`y_text(avg)`	`= 1/(pi – 0) int_0^pi e^(2x) cos (3x)\ dx`
	`~~ – 26.3`

`=> C`

The average value of the function with rule `f(x) = log_e(x + 2)` over the interval `[0,3]` is

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`=> E`

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`y_text(avg)`	`= 1/(3 – 0) int_0^3 log_e(x + 2)\ dx`
	`= (5log_e(5) – 2log_e(2) – 3)/3`

`=> E`