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3 years ago

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.

Mathematics

1 answer:

horrorfan [7]3 years ago

8 0

Substituting <em>x</em> = 0 directly gives the indeterminate form 0/0, so you can use l'Hopital's rule (and you'll have to do that twice):

$\displaystyle\lim_{x\to0}\frac{e^{6x}-6x-1}{x^2}=\lim_{x\to0}\frac{6e^{6x}-6}{2x}=\lim_{x\to0}\frac{36e^{6x}}2$

The limand is continuous everywhere, so you can plug in <em>x</em> = 0 to get 36•1/2 = 18.

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3 years ago

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zubka84 [21]

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y is 1/4 when x is -1 if I did interpret your equation right. Please see that I did.

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Step-by-step explanation:

If (-1,y) lies on the graph of $y=2^{2x}$ , then by substitution we have:

$y=2^{2\cdot -1}$ .

We just need to simplify to determine y:

$y=2^{2 \cdot -1}$

Multiply the 2 and -1:

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Use reciprocal rule for exponents to get rid of the negative:

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Step-by-step explanation:

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2 years ago

Trigonometry:

Trava [24]

A. The approximate height of the building is 100 m

B. We can use the arc length formula to obtain an approximation of BC since angle A is small.

The approximate height of the building is 100 m

To find the approximate height of the building, we consider the diagram.

From the diagram, we have that using trigonometry,

tanA = BC/AB

Now

A = 0.05 radians,
BC = height of building and
AB = 2 km = 2000 m

<h3 /><h3>Finding the value of BC</h3>

So, making BC subject of the formua, we have

BC = ABtanA

Substituting the values of the variables into the equation, we have

BC = ABtanA

BC =2000tan0.05

BC = 2000 × 0.05

BC = 100 m

So, the approximate height of the building is 100 m

We can use the arc length formula to obtain an approximation of BC since angle A is small.

<h3 /><h3>Arc Length Formula</h3>

We know that the arc length formula L = rФ where

r = radius and
Ф = angle in radians

<h3 /><h3>The approximate height</h3>

Now BC = ABtanA

We know that Ф ≅ tanФ when Ф is small.

<h3 /><h3>The comparison</h3>

So, BC = AB × A which is the arc length formula with

L = BC,
r = AB and
Ф = A

So, we can use the arc length formula to obtain an approximation of BC since angle A is small.

Learn more about approximate height of building here:

brainly.com/question/3144976

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2 years ago

How does 15.050 compare to 15.500

Varvara68 [4.7K]

15.050 < 15.500

notice that 500 is more than 50... so hope this helps a little bit !!!

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3 years ago

Read 2 more answers

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.​

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.