Ask question

Ask question

All categories

2 years 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

1 answer:

Angelina_Jolie [31]2 years 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

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

You might be interested in

Prove that if r is any rational number, then 3r2 − 2r + 4 is rational. The following properties may be used in your proof. Prope

ziro4ka [17]

Given:

Expression is

$3r^2-2r+4$

To prove:

If r is any rational number, then $3r^2-2r+4$ is rational.

Step-by-step explanation:

Property 1: Every integer is a rational number. It is Theorem 4.3.1.

Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.

Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.

Let r be any rational number.

We have,

$3r^2-2r+4$

It can be written as

$3(r\times r)-2r+4$

Now,

3, -2 and 4 are rational numbers by property 1.

$r^2=r\times r$ is rational by Property 3.

$3r^2\text{ and }-2r$ are rational by Property 3.

$3r^2+(-2r)+4$ is rational by property 2.

So, $3r^2-2r+4$ is rational.

Hence proved.

6 0

3 years ago

Triangle DEF has vertices D(−4, 1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the point (1, 1) as the point of

CaHeK987 [17]

Answer: $D'(-14,1);\ E'(4,7);\ F'(4,1)$

Step-by-step explanation:

Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':

$D_{O,k}(x,y)=(k(x-a)+a, k(y-b)+b)$

Where "O" is the center of dilation at (a,b) and "k" is the scale factor.

In this case you can identify that:

$(a,b)=(1,1)\\k=3$

Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:

Vertex D' → $(3(-4-1)+1,\ 3(1-1)+1)=(-14,1)$

Vertex E' → $(3(2-1)+1,\ 3(3-1)+1)=(4,7)$

Vertex F' → $(3(2-1)+1,\ 3(1-1)+1)=(4,1)$

6 0

3 years ago

Please help!! <br><br>is it 16?

sweet-ann [11.9K]

Answer:

area of trapezium: -

formula...

½(sum of parallel sides)×height=area

=>240=½(12+x)×12

=>240=(12+x)×6

=>240=60+6x

=>6x=240-60

=>6x=180

=>x=180/6

=>x=30cm

therefore, the value of x is 30 cm.

Step-by-step explanation:

hope it helps u

6 0

2 years ago

Hi please help , With solution if it's ok

Snowcat [4.5K]

<u>Answers </u><u>with </u><u>Method</u><u>:-</u>

1) Multiply the length value by 100,000.

$2.5 \: hm = 2.5 \times 100000$

$= >2.5 \: hm = 250000 \: mm$

2) For this, divide the length value by 1000.

$= > \frac{1800}{1000}$

$= > 1.8 \: dam$

3) For finding the approximate value, just multiply the value of length by 1.609.

$= >6450 \: m = (6450 \times 1.609) \: km$

$= > 10380.27 \: km$

4) Multiply the given mass value by 100.

$= > 1.2 \: kg = 1.2 \times 100$

$= > 1200 \: g$

5) Multiply the given value by 10,000.

$4.37 \: dag = 4.37 \times 10000$

$= > 43700 \: mg$

5 0

2 years ago

Type an equation that has the same slope as 2x 3y = 8 and the %3D e same y-intercept as -3-4y+2=0

alexandr402 [8]

Answer:

s

Step-by-step explanation:

5 0

2 years ago