Kindly answer the first question . LCM of 20,35 and 30
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Answer:
(B)
General Formulas and Concepts:
<u>Calculus</u>
Limits
Derivatives
- The definition of a derivative is the slope of the tangent line.
Derivative Notation
Instantaneous Rates
- Tangent Line:
Step-by-step explanation:
Since we are trying to find a <em>rate</em> at which W(t) changes, we must find the <em>derivative</em> at <em>t</em> = 3.
We are given 2 close answer choices that would have the same <em>numerical</em> answer but different <em>meanings</em>:
- (A)
- (B)
If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the <em>rate</em> at which the volume would be changing and it is not a derivative.
If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a <em>derivative</em> at <em>t</em> = 3, and a derivative tells us what <em>rate</em> something is changing.
∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when <em>t</em> = 3.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Step-by-step explanation:
Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.
For example,
Set the expression in the denominator equal to 0, because you can't divide by 0.
So the vertical asymptote is x=5.
Disclaimer if you see something like this
x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.
Horizontal:
If we have a function like this
We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.
Remember a constant can be represent by
For example,
And so on,
and
So our equation is basically
Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.
So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.
Consider the function
As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator
So in this case,
Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.