CALCULUS: Which of the following functions grows the fastest as x goes to infinity?
1 answer:
Answer:
It is A. 2^x
Step-by-step explanation:
For relative rates of growth, we know: Log < Poly < Exponential.
This rules out B, C, and D quickly. Although, if you do L'Hôpital's rule, it might seem like A & D are very comparable. However, if you continually took the derivative of 2^x and x^20, eventually x^20 would equal zero, while 2^x would still be a variable. So, you would have:
∞
When the limit of x as it approaches infinity is infinity, then f(x) grows at a faster rate than g(x).
Also, by looking at the graph (which is attached), you can see that 2^x grows faster than x^20.
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Option A : 25° C
Option C : -43° C
Option E : 0° C
Explanation:
It is given that the Methanol is in liquid form if its temperature is between -93.9°C and 64.96°C.
Let x represents the Methanol's temperature. Writing the temperature in interval notation, we have,
Now, let us determine from the given options that the temperatures at what are all the temperatures the methanol will be in liquid form.
Option A: 25° C
It is obvious that the 25° C lies in the interval
Hence, at 25° C Methanol will be in liquid form.
Thus, Option A is the correct answer.
Option B: -95° C
We can see that the temperature -95° C does not lie in the interval
Hence, at -95° C Methanol will not be in liquid form.
Thus, Option B is not the correct answer.
Option C: -43° C
We can see that the temperature -43° C lies in the interval
Hence, at -43° C Methanol will be in liquid form.
Thus, Option C is the correct answer.
Option D: 67° C
We can see that the temperature 67° C does not lie in the interval
Hence, at 67° C Methanol will not be in liquid form.
Thus, Option D is not the correct answer.
Option E: 0° C
We can see that the temperature 0° C lies in the interval
Hence, at 0° C Methanol will be in liquid form.
Thus, Option E is the correct answer.
Option F: 89° C
We can see that the temperature 89° C does not lie in the interval
Hence, at 89° C Methanol will not be in liquid form.
Thus, Option F is not the correct answer.