Find the equation of the line tangent to the graph of
at
We can use
[link] , but as we have seen, the results are the same if we use
[link] .
We now know that the slope of the tangent line is
To find the equation of the tangent line, we also need a point on the line. We know that
Since the tangent line passes through the point
we can use the point-slope equation of a line to find the equation of the tangent line. Thus the tangent line has the equation
The graphs of
and
are shown in
[link] .
The type of limit we compute in order to find the slope of the line tangent to a function at a point occurs in many applications across many disciplines. These applications include velocity and acceleration in physics, marginal profit functions in business, and growth rates in biology. This limit occurs so frequently that we give this value a special name: the
derivative . The process of finding a derivative is called
differentiation .
Definition
Let
be a function defined in an open interval containing
The derivative of the function
at
denoted by
is defined by
provided this limit exists.
Alternatively, we may also define the derivative of
at
as
Now that we can evaluate a derivative, we can use it in velocity applications. Recall that if
is the position of an object moving along a coordinate axis, the
average velocity of the object over a time interval
if
or
if
is given by the difference quotient
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
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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,
