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2 years ago

Please help: Find an equation of a line that is tangent to the graph of f and parallel to the given line.

Mathematics

1 answer:

slamgirl [31]2 years ago

5 0

⚘Refer to the attachments for complete solution!!~

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

<h3>Our equations are:</h3>

y= 3x+2 and y=3x-2

<h3>Our y-intercepts are:</h3>

-2 and 2

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Median of 70 61 87 85 72 65 86 80 90 60 63 81 75 77 67

liberstina [14]

I am pretty sure that the median is 80, correct me if I'm wrong :)

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3 years ago

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Hiiii.. please help me with this limit question

Alenkasestr [34]

Answer:

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

Solving with L'Hopital's rule:

If we plug in x = 0, the limit evaluates to 0/0. So using L'Hopital's rule:

lim(x→0) [ cos(π cos²x) (-2π cos x sin x) ] / 2x

lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

-π/2 lim(x→0) [ cos(π cos²x) sin(2x) ] / x

Again, the limit evaluates to 0/0. So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

-π/2 lim(x→0) [ 2 cos(π cos²x) cos(2x) + π sin(π cos²x) sin²(2x) ]

-π/2 (-2)

8 0

3 years ago

At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today. How much more did it snow yesterday than to

barxatty [35]

It snowed $\frac{3}{10}$ foot more yesterday than today

Solution:

Given that, At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today

From given information,

$\text{Snowed yesterday } = \frac{1}{2} \text{ foot }\\\\\text{Snowed today } = \frac{1}{5} \text{ foot }$

To find: how much more did it snow yesterday than today

So we have to find the difference between snowed yesterday and today

$\text{Difference} = \text{Snowed yesterday } - \text{ snowed today }\\\\\text{Difference} = \frac{1}{2} - \frac{1}{5}\\\\\text{Difference} = \frac{1 \times 5}{2 \times 5}-\frac{1 \times 2}{5 \times 2}\\\\\text{Difference} = \frac{5}{10}-\frac{2}{10}\\\\\text{Difference} =\frac{3}{10}$