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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.

You might be interested in
Which expressions are equivalent to (5⋅x)⋅3 ? Drag and drop the equivalent expressions into the box.
marysya [2.9K]
<h2>Greetings!</h2>

Answer:

3⋅(5⋅x)

5⋅(x⋅3)

15x

Step-by-step explanation:

As the values are inside the brackets, it does not matter what side the (x3) is on, so 3⋅(5⋅x) is equivalent.


Multiplying the contents of the brackets in the third one (x * 3) by 5 gives the same value as 3 * (x * 5) so 5⋅(x⋅3) is also equivalent.


On multiplying the brackets out:

5 * x = 5x

5x * 3 = 15x

So 15x is also equivalent.


<h2>Hope this helps!</h2>
3 0
3 years ago
Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A
alekssr [168]

Answer:

\theta_{CAB}=128.316

\theta_{ABC}=25.842

\theta_{BCA}=25.842

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}

AB= \sqrt{(-3-1)^2+(0-3)^2}=5

BC= \sqrt{(1-1)^2+(3-(-3))^2}=9

CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}

\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}

\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}

\theta_{CAB}=\arccos{-\dfrac{0.62}}

\theta_{CAB}=128.316

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}

\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)

\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)

\theta_{ABC}=\arcsin{0.4359}\right)

\theta_{ABC}=25.842

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

\theta_{BCA}=25.842

this can also be checked using the fact the sum of all angles inside a triangle is 180

\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180

25.842+128.316+25.842

180

6 0
3 years ago
Read 2 more answers
Can anyone help please? No links cause I can’t see them.
tamaranim1 [39]

Answer:

Step-by-step explanation:

you have a right triangle with the hypotenuse of 41 and another side of 40

a=\sqrt{41^2-40^2}=\sqrt{1681-1600}=\sqrt{81}

a=9

5 0
3 years ago
Can someone pls explain!
zzz [600]

Answer: 70% is shaded. 7 are shaded and there is a total of 10. then you divide the answer would be 0.7 which is the same as 70%

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Please help me I’ve been struggling
Shalnov [3]
Your answer will be 5.
Hope this helps!
3 0
3 years ago
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