L'Hospital's Rule Lim X approaches 0 cot2x•sin6x

1 answer:

3 0

$\bf \lim\limits_{x\to 0}\ cot(2x)sin(6x)\implies \lim\limits_{x\to 0}\ \cfrac{cos(2x)}{sin(2x)}sin(6x)\\\\
-----------------------------\\\\
\underline{LH}\qquad \cfrac{-2sin(2x)sin(6x)+cos(2x)6cos(6x)}{2cos(2x)}
\\\\\\
\lim\limits_{x\to 0}\ \cfrac{-2sin(2x)sin(6x)+cos(2x)6cos(6x)}{2cos(2x)}
\\\\\\
\lim\limits_{x\to 0}\ \cfrac{-0\cdot 0+1\cdot 6\cdot 1}{2\cdot 1}\implies \cfrac{6}{2}\implies 3$

You might be interested in

6 (r - 4) + r + 30 - 7r

GrogVix [38]

6r-24+r+30-7r (the we divide the regular numbers on one side and the others on the other side)Like this:
(6r+r-7r)+(-24+30)
(7r-7r)+6
And the final answer is 6

8 0

3 years ago

What weight of dry substance is in 150g of a 3% substance solution? What weight of an 8% solution can we have with the same weig

Pavlova-9 [17]

The answers are: 4.5 g and 56.25 g respectively.

Since the first type of measurement in this question is weight or mass, I'll suppose that the percentage concentration is % mass/mass. For that type of concentration measurement, just multiply the percentage by the total mass to get the mass of the wanted material.
So 150 g * 3% = 150 g * 0.03 = 4.5g

For the 8% solution with the same amount of dry substance, use the ratio of percentages, multiplied by the mass of the first solution to get the wanted amount of new solution:
3/8 * 150 g = 56.35 g

5 0

2 years ago

there are five students in the lunch line. May is 48 inches tall, Ann is 45 inches tall ,Con is 42 inches tall ,Bell is 52 inche

kirill115 [55]

Bell is the tallest person at 52 inches, Con is the shortest person at 42 inches. So 54 - 42 = 12

6 0

2 years ago

Read 2 more answers

How many ways are there to distribute six different toys to three different children such that each child gets at least one toy?

Kruka [31]

Give two toys to each child

6 0

3 years ago

Can someone Answer this?

Misha Larkins [42]

Answer:

The limit of the function as x approaches 1 is ∞

Vertical asymptote; x = 1

Step-by-step explanation:

The graphical approach to evaluating limits involves graphing the function, the graph of the function $\frac{1}{(x-1)^{2} }$ is contained in the attachment below.

The red vertical line is the graph of x = 1. As we approach the line x = 1 from the left, the value of the function, that is y becomes large and large indefinitely. That is the value of the function approaches infinity. The same case applies when we approach the vertical line x = 1 from the right.

Also noticeable is the fact that the function approaches the line x = 1 asymptotically. The function gets closer and closer to this line but actually never touches it. Therefore, the line x = 1 is our vertical asymptote of the function given

7 0

3 years ago