Convert 0.888 into a fraction (the 8 is repeating)
1 answer:
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Answer:
See solutions for detail.
Step-by-step explanation:
a. is the instantaneous rate of change of volume given with respect to time, t.
The volume's rate of change is written as a function of time.
- is the rate of change in the height of water in the tank with respect to time, t.
b. is the only constant. Water flows into the constant at a constant rate, say
per minute.
c. is positive. Volume water in the take is increasing from time to time.
-The volume at time t=1 is greater than the volume at t=0, hence, it's a positive rate of change.
d. is a positive rate. The initial height of water in the tank is zero.
-The final height at time t is 0.25h. The height is increasing with time.
Hence, it is positive.
Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:
and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders: since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1