# Tagged Questions

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### Behaviour of the function $\ln(1+ x^2)$

Thus function has derivative equal to: $\frac{2x}{1+x^2}$. This indicates that it will flatten out while approaching infinity, ie, should have an asymptote. Yet, the function does not have any real ...
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### Calculus: tangents and limits

For 1), I know the graph has a tangent but I don't know how to explain. For 2), is the answer 0? Would anyone mind giving me the steps? For 3) and 4), I really have no idea.
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### Need help with finding domains, intercepts, max/min of function

Here is a picture for clarification of the question: So far, I have gotten this: the root is all non-negative numbers; x is greater than or equal to 0. In order to find the asymptotes I set the ...
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### Approaching of area and perimeter of a regular polygon to that of a circle

When regular polygon approaches to circle its area and perimeter also approaches to that of a circle. Can you graphically show that ?
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### Draw graph from limit

How do I draw the graph of a function when the limit is given? For example, how can I draw the graph of the following function: $$f(x)=\lim_{n\to∞ }\frac{x^{2n+1}}{x^{2n}+1}$$ if the value of x is ...
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### How do I graph this limit?

How do I graph this limit ? The function has a limit as $x$ approaches $2$ of $5$ but $f(2) =4$. Specifically, what does $2$ of $5$ mean? The problem also wants me to write piecewise equations.
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### Calculating slant asymptotes of radical function

I'm trying to calculate the slant asymptotes of the function $\sqrt{x^2+2x+2}$. I've found out that the gradients of the asymptotes are 1 for $x\rightarrow+\infty$ and -1 for $x\rightarrow-\infty$. ...
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### How do you find the vertical, horizontal and inclined asymptotes of a square root function?

The following question asks me to find all horizontal, vertical and inclined asymptotes for the following function: $f(x)=\sqrt{x^2+5x+1}$ I've learnt that to find vertical asymptotes, you let ...
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### Find the right-hand and left-hand behavior of $f(x)=\frac{3x^3-2x+5}{4}$ [closed]

I need the explanation on how to find the right-hand and left-hand behavior of $$f(x) = \frac{3x^3-2x+5}{4}$$
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### I can express this programmatically, how would this be expressed mathematically?

So, I have a project in school where I have to make a 2 point perspective drawing and give the equations for all the lines. I would like to make a dashed line(we don't have to but I want to), so I was ...
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### How to find the oblique asymptote of root of a function?

In a test example I'm solving, the question asks to find the oblique asymptote of the following function: $f(x) = \sqrt{4x^2+x+6}$ $x$ at $+\infty$ We have only learned how to do so with rational ...
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### Is there an asymptote in this graph?

In the 2nd graph, is there an asymptote? Thanks!
### How to find the limit of $\sin(f(x))$, given the graph of $f(x)$
The full question is uploaded here: http://imgur.com/EZekb Basically, given the graph shown in the image above, I thought that the limit of $\sin(f(x))$ would be $\sin(2)$, since the limit of just ...