Lim -> 0 sin(2x) /(x*cos(x) )

help

Answers

Answer 1

Answer: sin (2x) can be written like:sin (2x) = 2sin(x)cos(x)
substituting this expresion in the original one:sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x
taking limits, and noticing that lim as x->0 of sinx/x=1:lim 2sinx/x=2*1=2x->0

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Which is a factor of x2 + 8x – 48?

Which equation shows an example of the associative property of addition?a.(–4 + i) + 4i = –4 + (i + 4i)
b.(–4 + i) + 4i = 4i + (–4i + i)
c.4i × (–4i + i) = (4i – 4i) + (4i × i)
d.(–4i + i) + 0 = (–4i + i)

Answers

The associative property states that we can regroup the terms of an expression and obtain the same result.

We have then:

$a + (b + c) = (a + b) + c$

The expression that complies with this property is given by:

$(-4 + i) + 4i = -4 + (i + 4i)$

Answer:

An equation that shows an example of the associative property of addition is:

a. (- 4 + i) + 4i = -4 + (i + 4i)

The correct option is $\boxed{\bf option (a)}$ i.e., $\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}$ .

Further explanation:

Concept used:

The associative property of the addition states that the addition of numbers cannot affect by the grouping of the number.

$\boxed{A+\left({B+C}\right)=\left({A+B}\right)+C}$

Here, in the above equation the value of $A+\left({B+C}\right)$ is always equal to the value of $\left({A+B}\right)+C$ whether the grouping of number is changes or not.

Calculation:

Now check the option to get the answer.

First check option (a)

$\left({-4+i}\right)+4i=-4+\left({i+4i}\right)$

In the above equation the grouping of the number is changed.

Now check the values of left hand side and right hand side.

$\begin{aligned}\left({-4+i}\right)+4i&=-4+\left({i+4i}\right)\n-4+5i&=-4+5i\end{gathered}$

The value of LHS is same as RHS.

Therefore, option (a) is correct.

Now check option (b)

$(-4+i)+4i=4i+(-4i+i)$

The term $i$ should be associated with $4i$ but it is associated with $-4i$ .

Therefore the option (b) is incorrect.

Now check option (c)

$4i* (-4i+i)=(4i-4i)+(4i* i)$

The above expression does not follow any property.

Therefore the option (c) is incorrect.

Now check option (d)

$(-4i+i)+0=-4i+i$

The above expression follows additive property not associative property.

Therefore the option (d) is incorrect.

Thus, the correct option is $\boxed{\bf option (a)}$ i.e., $\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}$ .

Learn more:

1. A problem on simplification: brainly.com/question/573729

2. A problem on domain and range: brainly.com/question/3412497

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Simplification

Keywords: Associative property, equation, property, addition, associative property of Addition, additive property, grouping terms, left hand side, right hand side, LHS, RHS.

True or False:8. V 40 has an infinite non-repeating decimal expansion.
9. The number 0.56 is a rational number
10. 200 and 500 are integers.
11. All numbers with infinite decimal expansions are irrational.
12.
the numbers -8, -3, 5, 17 are all whole numbers.

Answers

Answer:

Below.

Step-by-step explanation:

8. True ( all numbers of the form √n where n is not a perfect square have this property)

9. True ( we can write it as 56/100 or 14/25).

10. True.

11. False. ( 1/3 is rational and its decimal form is 0.333............. )

12. False. ( negative numbers are not whole numbers).

work the area of a rectangle out but already knowing the area and needing to know the length as it is two centermeters more than the width, area being 469

Answers

the area of a rectangle is the length times width:
a = l*w
the length is 2 centimeters more than the width:
l = w + 2
express area in terms of width
a = l*w
a = (w + 2)w
a = w^2 + 2w
w^2 + 2w = 469
w^2 + 2w - 469 = 0
we can solve using the general quadratic formula:
w = (-2 +- √(4 + 1876))/2
w = (-2 +- 43.36)/2
we use the positive solution:
w = (-2 + 43.36)/2
w = 20.68
thus the width is 20.68 cm
l = w + 2 = 20.68 + 2
l = 22.68
and the length is 22.68 cm

The formula P = ns gives the formula for the perimeter of a regular polygon with n sides and side length s.What is the length of each side of a regular octagon with a perimeter of 54.4 cm? A regular octagon has 8 equal sides.

Answers

P= 54.4
n=8
s=?
Divide P(54.4) by n(8) and you get s(6.8).

It a grade 9 please help me do this I don’t really understand it at all

Answers

Final answer:

The question lacks specific details, making it impossible to provide a structured and detailed response designed to meet the student's needs.

Explanation:

As the student question has not provided specific details or context about the topic they're struggling with, it's impossible to provide a clear, factual, and step-by-step explanation targetted to their needs. It is highly recommended that the student provides more details about the subject or the exact problem they are encountering in their grade 9 course to receive a structured and effective response. To help you understand better, could you please provide the specific question or topic you need assistance with? That way, I can provide a step-by-step explanation and relevant examples to help you.

Learn more about Lack of detail in question here:

brainly.com/question/24618579

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A basketball player is shooting free throws blindfolded. He shoots in groups of 4 shots. Assume that it is equally likely that he will hit or miss a shot. Design and do a simulation to determine the probability that he will hit at least 75% of his shots within the groups. (Hint: Use coins.)

Answers

Let H represent hit and M represent miss, Then sample space

MMMM, MMMH, MMHM, MHMM, HMMM, MMHH, MHMH, HMMH, MHHM, HMHM, HHMM, MHHH, HMHH, HHMH, HHHM, HHHH

He hit at least 75% in 5 occasions.

Therefore, P(hit at least 75%) = 5/16

Answer:

Use 4 coins. Let heads = hit and tails = miss. Toss each coin and record the results in a table. Coin 1Coin 2Coin3Coin 4Set 1HHHHSet 2HTHHSet 3HHTHSet 4THTTSet 5

Repeat the coin tosses until you have recorded 50 sets of 4 tosses each. b. Count the successful outcomes—those with three or four heads. Coin 1Coin 2Coin3Coin 4SuccessSet 1HHHHxSet 2HTHHxSet 3HHTHxSet 4THTTSet 5

Step-by-step explanation:

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