# limit equaling zero at infinity

I have a problem where I found the percentage of cells as time approaches infinity to be $$\frac{100d}{c+d}$$. All parameters are positive constants. The question asks are there circumstances when this quantity can be zero? I think if $$d$$ is small and $$c$$ is large, the percentage is very close to zero. But if all parameters are positive is it true that the quantity can never actually be zero?

• Even if only $d > 0$ the percentage must be nonzero since a fraction is equal to zero exactly when the numerator is $0$. – nbritten Dec 6 '19 at 23:37

Yes, it is true that if $$c,d > 0$$, then $$\frac{100d}{c+d} > 0$$ (so it can't equal $$0$$).

• would you mind if I delete this problem? – user707991 Dec 6 '19 at 23:38
• I wouldn't mind. (Not sure if others would mind though.) – Minus One-Twelfth Dec 6 '19 at 23:39
• @user707991 Why are you deleting it? – Don Thousand Dec 6 '19 at 23:41

We have that

$$\frac{100d}{c+d}=0 \iff d=0$$

and

$$\lim_{d/c\to 0} \frac{100d}{c+d}=0$$

$$\lim_{c/d\to \infty} \frac{100d}{c+d}=0$$

and you are right since all quantities are positive the ratio can't never be zero.

• would you mind if I delete this problem? – user707991 Dec 6 '19 at 23:39
• No it is not aproblem of course, since you are asking that! Bye – user Dec 6 '19 at 23:40
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