# -8.2.59 Find eq for level surface

• MHB
• karush
In summary, the equation for a level surface is an important tool in scientific research, particularly in fields such as geology, oceanography, and physics. It is typically calculated using mathematical methods and allows scientists to model and understand various natural phenomena. Some real-world applications include creating maps and navigation systems, predicting ocean currents, and designing structures. However, the equation may have limitations due to simplifications and data availability.
karush
Gold Member
MHB
$\tiny{x4.01}$
$\textsf{Find an equation for the level surface of the function}$
$$f(x,y,z)=x+e^{y+z}$$
$\textsf{ that passes through the point}$
$$(1, \ln(4), \ln(9))$$

Last edited:
Basically, you want:

$$\displaystyle f(x,y,z)=f\left(1,\ln(4),\ln(9)\right)$$

So, what do you get?

MarkFL said:
Basically, you want:

$$\displaystyle f(x,y,z)=f\left(1,\ln(4),\ln(9)\right)$$

So, what do you get?

plug in would be

$f(1,\ln(4),\ln(9))=1+e^{\ln(4)+\ln(9)}=1+4 \cdot 9 =37$

Last edited:
karush said:
plug in would be

$f(1,\ln(4),\ln(9))=1+e^{\ln(4)+\ln(9)}=1+4 \cdot 9 =37$

Yes, so the equation of the level surface would be:

$$\displaystyle x+e^{y+z}=37$$

## What is the significance of "-8.2.59 Find eq for level surface" in scientific research?

The equation for a level surface is important in many fields of science, including geology, oceanography, and physics. It allows us to describe surfaces that have a constant value, such as sea level, or the height of a mountain range.

## How do you calculate the equation for a level surface?

The equation for a level surface is typically calculated using mathematical methods such as calculus or differential equations. The specific method used depends on the type of surface being studied and the data available.

## What is the purpose of finding the equation for a level surface?

The equation for a level surface allows scientists to model and understand various phenomena in the natural world, such as gravity, ocean currents, and topography. It also helps us make predictions and solve problems related to these phenomena.

## What are some real-world applications of the equation for a level surface?

The equation for a level surface has many practical applications, such as creating accurate maps and navigation systems, predicting the behavior of ocean currents for shipping and fishing industries, and designing structures that can withstand gravitational forces, such as dams and bridges.

## What are the limitations of the equation for a level surface?

The equation for a level surface is based on simplifications and assumptions about the natural world, so it may not always accurately model real-world phenomena. Additionally, it may be challenging to obtain accurate data for certain surfaces, making it difficult to calculate the equation.

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