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Nataly_w [17]
3 years ago
15

lim x rightarrow 0 1 - cos ( x2 ) / 1 - cosx The limit has to be evaluated without using l'Hospital'sRule.

Mathematics
1 answer:
zaharov [31]3 years ago
6 0

Answer with Step-by-step explanation:

Given

f(x)=\frac{1-cos(2x)}{1-cos(x)}\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-(cos^2{x}-sin^2{x})}{1-cos(x)})\\\\(\because cos(2x)=cos^2x-sin^2x)\\\\\lim_{x \rightarrow 0}f(x)=\lim_{x\rightarrow 0}(\frac{1-cos^2x}{1-cos(x)}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}(\frac{(1-cosx)(1+cosx)}{1-cosx}+\frac{sin^2x}{1-cosx})\\\\=\lim_{x\rightarrow 0}((1+cosx)+\frac{sin^2x}{1-cosx})\\\\\therefore \lim_{x \rightarrow 0}f(x)=1

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you work at a hair salon and get left a 35 tip on a 112 haircut and color service . What percent tip did your customer give you
levacccp [35]
31.25 percent of 112 is 35
7 0
3 years ago
You multiply two integers. You increase one of them by 1 and decrease the other
snow_tiger [21]

Integers are numbers without decimals

The integers could you have multiplied are 9 and 2

Let the numbers be x and y

So, we have:

\mathbf{x \times y}

Increase x by 1 and reduce y by 1.

So, we have

\mathbf{(x +1) \times (y -1) = 6 + xy }

Open brackets

\mathbf{xy -x + y - 1 = 6 + xy}

Subtract xy from both sides

\mathbf{ -x + y - 1 = 6}

Collect like terms

\mathbf{ -x + y = 6 + 1}

\mathbf{ -x + y = 7}

Rewrite as:

\mathbf{ y -x= 7}

The above means that, the difference between the integers is 7.

There are several integers that fit the above <em>description</em>;

One possibility is: 9 and 2

Read more about products at:

brainly.com/question/3208278

6 0
2 years ago
Maya is comparing ride-sharing company prices. Company M charges $1.75 per mile driven and a one-time trip fee of $5. Company N
BabaBlast [244]

Answer:

1.75x+5<2.5x+3

Step-by-step explanation:

4 0
3 years ago
Analyze the asymptotes of the function.
koban [17]

Answer:

vertical asymptote at x=-1

horizontal asymptote at y=0

Step-by-step explanation:

y=\frac{1}{x+1}

To find vertical asymptote we set the denominator =0 and solve for x

x+1=0 (subtract 1 from both sides)

x=-1

So, vertical asymptote at x=-1

To find horizontal asymptote we look at  the degree of both numerator and denominator

there is no variable at the numerator , so degree of numerator =0

degree of denominator =1

When the degree of numerator is less than the degree of denominator

then horizontal asymptote at y=0

5 0
3 years ago
When given an inverse variation, how do you find k?
atroni [7]

Considering an inverse proportional relationship, you find k taking a point (x,y), and multiplying the values of x and y.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For an inverse relationship, the function is:

y = \frac{k}{x}.

Then:

k = xy.

Which means that to find k, you take a point (x,y), and multiply the values of x and y.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

8 0
2 years ago
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