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rjkz [21]
3 years ago
5

Use​ l'Hôpital's Rule to find the following limit. ModifyingBelow lim With x right arrow 0StartFraction 3 sine (x )minus 3 x Ove

r 7 x cubed EndFraction ModifyingBelow lim With x right arrow 0StartFraction 3 sine (x )minus 3 x Over 7 x cubed EndFraction equals nothing ​(Type an exact​ answer.)
Mathematics
1 answer:
steposvetlana [31]3 years ago
8 0

Answer:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}=-\frac{1}{14}

Step-by-step explanation:

The limit is:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}=\frac{0}{0}

so, you have an indeterminate result. By using the l'Hôpital's rule you have:

\lim_{x \to 0} \frac{a(x)}{b(x)}= \lim_{x \to 0} \frac{a'(x)}{b'(x)}

by replacing, and applying repeatedly you obtain:

\lim_{x \to 0} \frac{3sinx-3x}{7x^3}= \lim_{x \to 0}\frac{3cosx-3}{21x^2}= \lim_{x \to 0}\frac{-3sinx}{42x}= \lim_{x \to 0}\frac{-3cosx}{42}\\\\ \lim_{x \to 0} \frac{3sinx-3x}{7x^3}=\frac{-3cos0}{42}=-\frac{1}{14}

hence, the limit of the function is -1/14

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Step-by-step explanation:

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3 years ago
Which justification describes the process?
tester [92]

Answer:

Option 1 - Using the Subtraction Property of Equality, 2 is subtracted from both sides of the equation.          

Step-by-step explanation:

Given : Process

Step 1: 4x + 2 = 10

Step 2: 4x = 8

To find : Which justification describes the process?

Solution :

From step 1 to step 2, we subtract 2 both sides

Step 1: 4x + 2 = 10

Subtracting 2 both side,

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So, The best justification is 'Using the Subtraction Property of Equality, 2 is subtracted from both sides of the equation'.

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4 0
3 years ago
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zlopas [31]

Answer:

Option D. Marcelina spends less that the intended amount of money and buy less than enough corn

Step-by-step explanation:

Let

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y ---> is the amount of yellow corn she buys

we know that

She needs to buy 50 kg of corn in total

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x+y=50 ----> equation A

She wants to spend $12 dollars total

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The solution of the system of equations is the intersection point both graphs

The solution is the point (30,20)

That means

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3 years ago
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7 0
3 years ago
Find the quotient 4/5 ÷3
Deffense [45]
 \frac{4}{5} divided by 3 = 4/15


Hope I Helped
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