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Featured 1 month ago

See below.

This differential equation is linear so it can be represented as the sum

The solution for

now supposing that

we get

Featured 3 weeks ago

We must use our log laws:

Now applying our knowledge of differentiating logs:

By using the chain rule...

Featured 3 weeks ago

Substitute

Using the fact that

Since

Using the fact that

Featured 3 weeks ago

The coordinates of the midpoint of

The gradient to the curve

At the point

The slope of the tangent at the point

Therefore,

The slope of the normal at the point

The equation of the normal at the point

When

The point

When

The point

The midpoint of

The equation of the curve is obtained by integrating the derivative, or by solving the differential equation

Plugging in the values of

The equation of the curve is

graph{(2y+x-17)(y+4sqrt(6-2x)-16)=0 [-22.17, 23.44, -4.57, 18.27]}

Featured 1 week ago

Write the function as:

Consider now the limit:

It is in the indeterminate form

As the limit is finite and the function

Featured yesterday

See below.

I hope it helps.

The partial derivative is intrinsically associated to the total variation.

Suppose we have a function

Fixing ideas, making

In our function-example we have

and then

Choosing

but generally

now making

so we can compute the total variation for a given function, by calculating the partial derivatives

Here, the quantities

In our example

NOTE

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