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221 Unit I Beginnings
A derivative
Limits are
221 Unit I Beginnings
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Preliminary understanding to development of the derivative
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Answers
1
Limits are
z scores
x values
z values
y values
2
A derivative
can be shown with a tangent line at a point
is slope at a point
all of the above
is instantaneous rate of change
3
Calculus is the study of
accumulation
microbes
instantaneous rates of change
teeth
4
Derivatives do NOT exist
at corners
at cusps
where the slope changes too rapidly
at the origin
5
The limit definition of the derivative
can show a secant line turning into a tangent line
is a combination of algebra, calculus and arithmetic work
requires that h approach zero
requires that the numerator approach one
6
A logarithm is
a derivative
an exponent
non-factorable
a limit
7
Continuity implies
no breaks/holes in drawing
there was a rational function
an asymptote exists
tracing the function without lifting the pencil
8
ARoC is
change over an interval
instantaneous rate of change
old divided by new
average rate of change
9
Exponential growth/decay
is linear
is instantaneous
indicates repeated multiplication
requires limits
10
An example of non-differentiability is
a root
the corner of the absolute value function
a radical function
zero
