final exam Flashcards
what rule do we use when we try to evaluate and it gives 0/0 or inf/inf
L’hopital rule
what happens when denominator is bigger than numerator
it will be 0
ln(x)
1/x
cos(0)
1
d/dx of cosx
-sinx
sin(0)
0
d/dx of sinx
cosx
in limits, sinx/x
its 1
what to do with LH
keep find doing derivative until it does not give 0/0 or inf/inf
a^3 - b^3
(a-b)(a^2+ab+b^2)
in limits, tanx
its sinx/cosx
in limits, if polynomials
ignores insignificant terms
in limits, if we look for HA
we use limit x->inf
in limits, if we look for VA
we use limit x->0
any power of 0
= 1
loga (b) = c
= a^c b
ln(1)
0
squeeze theorem
h(x) <_ f(x) <_ g(x)
d/dx of x
= 1
d/dx of e
= 0
d/dx of ln(u)
= u’/u
log,diff and inv trig: d/dx of a^u
= a^u . u’ . ln (a)
d/dx of e^u
= e^u . u’
in piecewise functions, if there’s a letter except x and y
have to make it the same and that letter = ?