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adell [148]
1 year ago
11

Given f(x)=e^-x^3 find the vertical and horizontal asymptotes

Mathematics
1 answer:
Aleonysh [2.5K]1 year ago
5 0

Given:

f\mleft(x\mright)=e^{-x^3}

To find the vertical and horizontal asymptotes:

The line x=L is a vertical asymptote of the function f(x) if the limit of the function at this point is infinite.

But, here there is no such point.

Thus, the function f(x) doesn't have a vertical asymptote.

The line y=L is a vertical asymptote of the function f(x) if the limit of the function (either left or right side) at this point is finite.

\begin{gathered} y=\lim _{x\rightarrow\infty}e^{-x^3} \\ =e^{-\infty} \\ y=0 \\ y=\lim _{x\rightarrow-\infty}e^{-x^3} \\ y=e^{\infty} \\ =\infty \end{gathered}

Thus, y = 0 is the horizontal asymptote for the given function.

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1
Lera25 [3.4K]
Assuming the function is

f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}

For f(x) to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)
\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)
\iff2=b+c

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

f'(x)=\begin{cases}2&\text{for }x1\end{cases}

\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)
\iff2=2b+c

Now we solve for b and c:

\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2
5 0
3 years ago
The number of turtles in a pond is four more than twice the number of crocodiles.
cluponka [151]

twice the number is multiplying

 so it would be 2c then add 4 more

 so 2c+4 is the correct equation.

 Answer is B

3 0
3 years ago
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I'm not really good at these types of questions would really appreciate some help.
Lunna [17]

Answer:

Thanks!

Step-by-step explanation:

The falling leaves and the draining of the pool signal an end and parallel the end of the illusion and the end of Gatsby's life.

7 0
3 years ago
Find x and y pls<br> pls write 20 characters
Ymorist [56]

Answer:

n = 135   m = 45

Step-by-step explanation:

N is 135 and m is on a strait line (180) so if you do 180 - 135 you will get the answer for m.

Hope this helped.

4 0
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Katarina [22]

Answer:D

Step-by-step explanation:

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