# Linked Questions

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### Limit of $y$ if limit of $y+y'$ goes to $0$? [duplicate]

Let $y$ be a differentiable function on $\mathbb{R}$. If $$\lim_{x\rightarrow \infty}(y(x)+y'(x))=0$$ Then how does one show that $$\lim_{x\rightarrow \infty}y(x)=0$$ I'd appreciate some help on this ...
1answer
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### What can we say about $\alpha$ if $\lim_{x\to \infty}f(x)=1$ and $\lim_{x\to \infty}f'(x)=\alpha$ for a differentiable function $f$ on $\mathbb{R}$? [duplicate]

For what values of $\alpha$ would the given conditions hold? I don't know how to proceed.
0answers
114 views

### finite $\lim_{x \rightarrow +\infty} f(x)$ and $\lim_{x \rightarrow +\infty} f'(x)$. Then $\lim_{x \rightarrow +\infty} f'(x) = 0$ [duplicate]

Let f be twice differentiable function on R with finite $\lim_{x \rightarrow +\infty} f(x)$ and $\lim_{x \rightarrow +\infty} f'(x)$. Then $\lim_{x \rightarrow +\infty} f'(x) = 0$ I don't know how ...
1answer
46 views

Let $f$ be a continuously differentiable function on $\mathbb{R}$ such that both the limits $\lim_{x \rightarrow \infty} f(x)$ and $\lim_{x > \rightarrow \infty} f'(x)$ exist and are finite. Is $\... 2answers 31 views ### A differentiable function with itself and its derivative converge to constants, can we conclude its derivative converge to zero [duplicate] I have been struggled with the following problem. Suppose that$f$is differentiable on$(0, \infty)$. If we have$\lim_{x \rightarrow \infty} f(x) = c_1$and$\lim_{x \rightarrow \infty} f'(x) = c_2$... 6answers 13k views ### If a function has a finite limit at infinity, does that imply its derivative goes to zero? I've been thinking about this problem: Let$f: (a, +\infty) \to \mathbb{R}$be a differentiable function such that$\lim\limits_{x \to +\infty} f(x) = L < \infty$. Then must it be the case that$\...

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