A tangent plane to a surface does not always exist at every point on the surface. Consider the function
The graph of this function follows.
If either
or
then
so the value of the function does not change on either the
x - or
y -axis. Therefore,
so as either
approach zero, these partial derivatives stay equal to zero. Substituting them into
[link] gives
as the equation of the tangent line. However, if we approach the origin from a different direction, we get a different story. For example, suppose we approach the origin along the line
If we put
into the original function, it becomes
When
the slope of this curve is equal to
when
the slope of this curve is equal to
This presents a problem. In the definition of
tangent plane , we presumed that all tangent lines through point
(in this case, the origin) lay in the same plane. This is clearly not the case here. When we study differentiable functions, we will see that this function is not differentiable at the origin.
The diagram for the linear approximation of a function of one variable appears in the following graph.
The tangent line can be used as an approximation to the function
for values of
reasonably close to
When working with a function of two variables, the tangent line is replaced by a tangent plane, but the approximation idea is much the same.
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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