4 years ago

What is the answer to this question?

Mathematics

1 answer:

Anna35 [415]4 years ago

6 0

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

steposvetlana [31]

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

8 0

3 years ago

What is the area of a circle with a radius of 13 millimeters? (Use 3.14 for Pi.)

pav-90 [236]

Step-by-step explanation:

Given

Radius (r) = 13 mm

Area of the circle

= πr²

= 3.14 * 13 *13

= 530.66 mm²

Hope it will help :)

5 0

3 years ago

find all the factors of 38,39 and 40?.do they have any factors in common.explain how you can tell if some numbers have factors i

stellarik [79]

Answer:

It is 1

Step-by-step explanation:

They all have different factors and the only one is 1.

4 0

4 years ago

ron walks 0.5 mile on the track in 10 minutes . steve walks 0.25 mile on the track in 6 minutes . find the unit rate for each wa

mihalych1998 [28]

Ron walks faster because his unit rate is 20 and steve's unit rate is 24.

3 0

3 years ago

3x over 10 = 1,290 <br> please help

MAVERICK [17]

3x/10= 1290

Mutiply by 10 for both sides

3x/10*10= 1290*10

Cross out 10 and 10 , divide by 10 and then becomes 3x

3x=12900

divide by 3 for both sides

3x/3= 12900/3

Cross out 3 and 3 , divide by 3 and then becomes x

x= 4300

Answer: x= 4300

8 0

4 years ago