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Calculus, power series, bounded derivative, closed bounded interval…
Calculus
continuity
uniform continuity
sequencial or e delta
on a set
then also on its subset
a and b no intersection
union pe uniform continiuity
impiles continiuty
lipshitzc continous
Limits
Sandwhich theorem
talyors theorem
Talyor series
infinitely differentiable function
still may not be convergent
even if convergent it may not be equal to function
if Remainder term goes to zero
then function = talor series
sufficient condition
all the derivatives are bounded
maclaurian series
derive the nth derivative test
derive the l hospital rule
see the pattern the derivatives and then connect that with N and use pmi to verify that
derivative
power series
properties
useful to find the taloyr series of a function
multiplication
division
term by term diffrentiation
term by term integration
application
solving ordinary differential equations
integration
non integrable function
differentiation
radius of convergence
1/limsup|a|1/n
revise the limsup
theorems of limits
not the maximum interval of convergence
because we don't include the end points in it
convergence
radius convergence
check when boundary points of the interval x = radius convergence
bounded derivative
closed bounded interval continiuity
inverse function therorm