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Katarina [22]
1 year ago
7

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 e3x − 1 −

3x x2
Mathematics
1 answer:
Angelina_Jolie [31]1 year ago
8 0

It looks like the limit is

\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2}

L'Hôpital's rule works in this case; applying it twice gives

\displaystyle \lim_{x\to0} \frac{e^{3x} - 1 - 3x}{x^2} = \lim_{x\to0} \frac{3e^{3x} - 3}{2x} = \lim_{x\to0} \frac{9e^{3x}}{2} = \boxed{\frac92}

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What is 9/16 x 12/13 and 7/10 x 5/28
lilavasa [31]

Answer:

1. 9/16 * 12/13 = 27/52

2. 7/10 * 5/28 = 1/8

Step-by-step explanation:

1.

9 / 16 * 12/13

9 * 12 = 108

16 * 13 = 208

108 / 208

Simplify:

27/52


2.

7 / 10 * 5 / 28

7 * 5 = 35

10 * 28 = 280

Simplify:

1/8

8 0
3 years ago
Read 2 more answers
Car A's fuel efficiency is 34 miles per gallon of gasoline, and car B's fuel efficiency is 23 miles per gallon of gasoline. At t
Verdich [7]

Answer:

22 more gallons.

Step-by-step explanation:

Given:

Car A's fuel efficiency is 34 miles per gallon of gasoline.

Car B's fuel efficiency is 23 miles per gallon of gasoline.

Question asked:

At those rates, how many more gallons of gasoline would car B consume than car A on a 1,564 miles trip?

Solution:

<u>Car A's fuel efficiency is 34 miles per gallon of gasoline.</u>

<u>By unitary method:</u>

Car A can travel 34 miles in = 1 gallon

Car A can travel 1 mile in = \frac{1}{34} \ gallon

Car A can travel 1564 miles in = \frac{1}{34} \times1564=46\ gallons

<u>Car B's fuel efficiency is 23 miles per gallon of gasoline.</u>

Car B can travel 23 miles in = 1 gallon

Car B can travel 1 mile in = \frac{1}{23} \ gallon

Car B can travel 1564 mile in = \frac{1}{23} \times1564=68\ gallons

We found that for 1564 miles trip Car A consumes 46 gallons of gasoline while  Car B consumes 68 gallons of gasoline that means Car B consumes 68 - 46 = 22 gallons more gasoline than Car A.

Thus, Car B consumes 22 more gallons of gasoline than Car A consumes.

<u />

6 0
3 years ago
There are 3 cans that store 9 tennis balls. Consider the number of balls per can.
Arada [10]

Answer:

27

3*9=27

i think thats right

3 0
3 years ago
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if a quadratic equation with real coefficients has a discriminant of -36 then what type of roots does it have
Aleks04 [339]

Step-by-step explanation:

We have,

If a quadratic equation with real coefficients has a discriminant of -36.

The general form of quadratic equation is :

ax^2+bx+c=0

The discriminant of this equation is : D=b^2-4ac

If D=0, it will have 1 real roots

If D>0, it will have 2 real roots

If D<0, it will have no real roots

We have,

D = -36 < 0, so, the quadratic equation will have no real roots.

5 0
3 years ago
Please each value on the number line!
iren2701 [21]
1,4,2,3 is the order
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3 years ago
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