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JulsSmile [24]
3 years ago
15

The limit as h approaches 0 of (e^(2+h)-e^2)/h is ?

Mathematics
1 answer:
Whitepunk [10]3 years ago
3 0
<span>If you plug in 0, you get the indeterminate form 0/0. You can, therefore, apply L'Hopital's Rule to get the limit as h approaches 0 of e^(2+h),
which is just e^2.
</span><span><span><span>[e^(<span>2+h) </span></span>− <span>e^2]/</span></span>h </span>= [<span><span><span>e^2</span>(<span>e^h</span>−1)]/</span>h

</span><span>so in the limit, as h goes to 0, you'll notice that the numerator and denominator each go to zero (e^h goes to 1, and so e^h-1 goes to zero). This means the form is 'indeterminate' (here, 0/0), so we may use L'Hoptial's rule:
</span><span>
=<span>e^2</span></span>
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That which is equivalent to tanθ is A sinθ/cosθ

To answer the question, we need to know what tanθ is

<h3>What is tanθ?</h3>

Tanθ is a trigonometric identity which is the tangent of the angle .

Now, from the unit circle, with radius, r = 1, we have that tanθ = y/x.

Also, the sine of the angle θ is sinθ = x/1 = x

And also, the cosine of the angle θ is cosθ = y/1 = y

Since we have that

  • tanθ = y/x,
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Substituting the values of the variables y and x into tanθ, we have

tanθ = y/x

tanθ = sinθ/cosθ

So, that which is equivalent to tanθ is A sinθ/cosθ

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5 0
2 years ago
The height of a cylinder is 10 and the area of a base is 36 pi square units. What
ollegr [7]

Answer:

1130.97336 units^3

Step-by-step explanation:

The volume of a cylinder can be found using:

v=\pi r^2h

We have the area of the base, but not the radius

a=\pi r^2

We know the area is 36\pi, so we can substitute that in for a

36\pi =\pi r^2

We want to find r, so we need to isolate it

Divide both sides by pi

36=r^2

Take the square root of both sides

6=r

Now we know the radius, and can substitute it into the volume formula, and we can substitute the height (10) in

v=\pi r^2h

v=\pi 6^210

Solve the exponent

v=\pi 36(10)

v=\pi 360

v=1130.97336

The volume is 1130.97336 units^3

6 0
3 years ago
What is the intersection when you graph the following equations:
Natasha2012 [34]

Answer:

its -2x

Step-by-step explanation:

7 0
3 years ago
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Which expression best represents the product of quantities a, b, and H?
Aleks [24]

Answer:

C) abH

Step-by-step explanation:

a × b × H

= abH

The answer is option C

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3 years ago
Jacks living room is 16 feet by 20 feet long. if a scale drawing of his living room uses a scale of 3/4 inches= 6 feet, find the
Juli2301 [7.4K]

Answer:

40 inches

Step-by-step explanation:

16×20=320

320÷6=53.33

53.33×3=159.99

159.99÷4=39.9975

39.9975 rounded would be 40

6 0
2 years ago
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