3
votes
2answers
89 views

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 ...
2
votes
2answers
35 views

Draw a function $g$ such that $g$ is defined on the interval $[-9,9]$

Sketch a function $g$ such that $g$ is defined on the interval $[-9,9]$ and satisfies the following properties: a) $g(-5) = 1$, but $\lim_{x \to -5} g(x)$ does not exist. b) $\lim_{x \to 1} g(x) = ...
0
votes
2answers
28 views

$y = xe^{−1/|x|}$ for $−∞ < x < ∞$

(a) Let $f(x) = x − xe^{−1/x}, x > 0$. Show that f(x) is an increasing function on $(0,∞),$ and $\lim_{x→∞} f(x) = 1$. (b) Using part (a) and calculus, sketch the graphs of $y = x−1, y = x, y = x ...
3
votes
3answers
86 views

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.
1
vote
1answer
47 views

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 ...
0
votes
1answer
66 views

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 ?
2
votes
1answer
447 views

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 ...
0
votes
2answers
233 views

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.
0
votes
1answer
489 views

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 $x\rightarrow-\infty$. ...
2
votes
3answers
3k views

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 ...
0
votes
1answer
103 views

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 $$ f(x) = \frac{3x^3-2x+5}{4} $$
5
votes
4answers
161 views

How can a point of symmetry have a slope which isn't either $0$ or $±\infty$?

I've got a bit of a doubt with a question I'm solving. It goes like this: For $a>0$, let $f:[-4a,4a] \to R$ be an even function such that $f(x) = f(4a - x) \hspace{2 mm}\forall x \in [2a, ...
1
vote
3answers
190 views

Plot of x^(1/3) has range of 0-inf in Mathematica and R

Just doing a quick plot of the cuberoot of x, but both Mathematica 9 and R 2.15.32 are not plotting it in the negative space. However they both plot x cubed just fine: ...
0
votes
1answer
98 views

Is the line really passing through point $a$?

I've answered an exercise on Stewart's Essential Calculus, he asks me to sketch a graph of an example of a function $f$ that satisfies all of the given conditions below: $\lim_{x\rightarrow ...
2
votes
2answers
75 views

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 ...
2
votes
4answers
3k views

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 ...
0
votes
1answer
71 views

Is there an asymptote in this graph?

In the 2nd graph, is there an asymptote? Thanks!
3
votes
1answer
341 views

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 ...
0
votes
1answer
62 views

Compute lim from Graph

This image is from my textbook. In my textbook, there is one question: Does it makes sense to compute lim(T->50) R(T). In this graph, I don't know lim is 1.5 or 0. Please tell me and explain for ...