The critical points are at x = 1 and x = 4 giving you the intervals (-inf, 1), (1, 4) and (4, inf).
By substituting x values in these 3 intervals, you can see that f'(x) is positive in the first and third intervals and negative in the second interval.
This means that f(x) is increasing in the first and third intervals and decreasing in the second interval.
The answer is D.
Answer:
x = 17
Step-by-step explanation:
These angles are supplementary so (2x + 5) + (8x = 5) = 180 then you just do the algebra
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Answer:
Anything in the form x = pi+k*pi, for any integer k
These are not removable discontinuities.
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Explanation:
Recall that tan(x) = sin(x)/cos(x).
The discontinuities occur whenever cos(x) is equal to zero.
Solving cos(x) = 0 will yield the locations when we have discontinuities.
This all applies to tan(x), but we want to work with tan(x/2) instead.
Simply replace x with x/2 and solve for x like so
cos(x/2) = 0
x/2 = arccos(0)
x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k
x = pi + 4pi*k or x = -pi + 4pi*k
Where k is any integer.
If we make a table of some example k values, then we'll find that we could get the following outputs:
- x = -3pi
- x = -pi
- x = pi
- x = 3pi
- x = 5pi
and so on. These are the odd multiples of pi.
So we can effectively condense those x equations into the single equation x = pi+k*pi
That equation is the same as x = (k+1)pi
The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).
Answer: B
$10,390.75
Step-by-step explanation:
Given that the lease = $291 per month
Lease pay = 291 × 24 = $6984
Time = 24 months
down payment = $458.
The lease allows for 12,000 miles per year and includes a $0.35 per mile charge for miles driven in excess of that amount.
For the car to be driven a total of 32,425 miles.
Excess = 32425 - 24000 = 8425 miles
Charges = 0.35 × 8425 = $2948.75
The cost for two years for this vehicle will be
2948.75 + 458 + 6984 = $10390.75