Calculus homework studying for the test: Find K such that

• huan.conchito
In summary, Daniel suggests looking for a continuous function that satisfies the following equation: f(x) = 2 + sin(x) for all x in the domain. He suggests solving for "k" such that this equation is satisfied.
huan.conchito
Calculus homework studying for the test: Find K such that this is continious

$$f(x)=\left\{\begin{array}{cc}k&\mbox{ if }x=0\\2+\frac{Sin(x)}{x} &\mbox{ if }x\neq 0\end{array}\right$$

i have no clue how to find such a k that this is continious

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well, from your question I see no reason why I can't choose any $k$ that I like. Are you sure that's all there is to it?

Perhaps you are trying to make $f(x)$ continuous?

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U didn't say what the problem wa about.I assume it required that the brach function would be continuous on R...Which means point "x=0",too.

What's the condition for an univariable function defined on a domain $\matcal{D}\subseteq \mathbb{R}$ to be continuous in a point $x \in \mathcal{D}$...?

Daniel.

Thats all the question says "find k such that this is continious"

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Then the aswer is $k\in \mathbb{R}$,which means an arbitrary #...

Daniel.

Thats all the question says "find k such that"
blah blah

perhaps you should elaborate on the "blah blah," verbatim if possible. I find it highly doubtful that that is what it was asking for in a calculus course.

huan.conchito said:
f(x) = {k if x=0 if x == 0
{2+(sinx)/x if x =/= 0

i have no clue how to find such a k
Well, IF the objective is to find "k" such that "f(x)" is continuous, what "k" would satisfy that condition??

HINTS #1 & #2:

$$1: \ \ \ \ \lim_{x \longrightarrow 0} \, f(x) \ = \ f(0)$$

$$2: \ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \color{red} \mathbf{?}$$

~~

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Well first like this:

$$f(x)=\left\{\begin{array}{cc}k,&\mbox{ if }x=0\\2+\frac{Sin(x)}{x}, &\mbox{ if }x\neq 0\end{array}\right$$

Not too hard, check out the syntax in the editor.

Then just do what Xanthym said to assure continuity.

Maybe the function needs to be differentiable...

Daniel.

the problem is exactly like salty dog wrote it.
and it says
"Find K such that this is continious"

$$2: \ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \color{red} \mathbf{2?}$$

xanthym said:
Well, IF the objective is to find "k" such that "f(x)" is continuous, what "k" would satisfy that condition??

HINTS #1 & #2:

$$1: \ \ \ \ \lim_{x \longrightarrow 0} \, f(x) \ = \ f(0)$$

$$2: \ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \color{red} \mathbf{?}$$

~~

Incorrect.Check that "sin" limit again.

Then u can get conclude what K needs to be...

Daniel.

the limit = 0, so K must be 0?

huan.conchito said:
the limit = 0, so K must be 0?

lim {x->0} sin x/x = 1.

so k must be 3 ?

Deleting your previous post and then reposting exactly the same thing is a rather cunning way to get an answer

Anyways, yes, that's fine.

Correct. If you are unsure why $$\ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \ \mathbf{1}$$ you might have a look at the Taylor expansion of $$sin(x)$$ .

Correct. If you are unsure why $$\ \ \ \ \lim_{x \longrightarrow 0} \, \left (2 \ + \ \frac{\sin(x)}{x} \right ) \ = \ \ \mathbf{1}$$ you might have a look at the Taylor expansion.

You mean $3$ .

We have a thread on the "sinc" limit.It has some good posts.

Daniel.

1. What is Calculus and why is it important?

Calculus is a branch of mathematics that deals with rates of change and accumulation. It is important because it provides a powerful set of tools for solving real-world problems in fields such as physics, engineering, economics, and more.

2. How do I find K in a calculus problem?

Finding K in a calculus problem typically involves using the given information and applying appropriate formulas and techniques. It is important to carefully read and understand the problem before attempting to find K, and to check your work for accuracy.

3. What are some common techniques for studying for a calculus test?

Some common techniques for studying for a calculus test include practicing problems, reviewing notes and class materials, creating study guides or flashcards, and seeking help from a tutor or classmate. It is also important to get enough rest and manage stress levels before the test.

4. How can I improve my understanding of calculus concepts?

Improving your understanding of calculus concepts involves actively engaging with the material, asking questions, and seeking help when needed. It can also be helpful to connect calculus concepts to real-world applications and to practice problems regularly.

5. What should I do if I am struggling with my calculus homework or studying for a test?

If you are struggling with your calculus homework or studying for a test, it is important to seek help from your teacher or a tutor. You can also try breaking down the material into smaller, more manageable chunks and practicing regularly. Don't be afraid to ask questions and seek clarification if needed.

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