Unit 6a 6.2-6.6 Flashcards
Fundamental theorem of calculus
if g(x)=inta->x f(t) dt where a is a constant and f is cont by a then g’(x) = f(x)
lnx =
int1->x 1/t dt
int 1/u du =
ln|u| + c
The uniqueness theorem
If f’(x) = g’(x) for all x and f(a) = g(a) for one value x=a then f(x) = g(x) for all x
basically: if two functions have the same derivative everywhere and they also have a point in common then they are the same function
logbx =
logax/logab = lnx/lnb
b^x =
b^xlnb
int b^u du =
b^u/lnb + c
l’Hospital’s Rule
If f(x) = g(x)/h(x) and if limx->c g(x)=limx->ch(x)=0
then limx->cf(x) =
limx->c g’(x)/h’(x)
General knowledge:
a. ln(e^x) =
b. e^lnx =
c. b^y=x =
d. log(b)b, lne =
e. log(b)b^x=, lne^x
f. ln1 =
g. log(b) 0 =
h. 1/0 is not
i. a/oo =
j. oo/a =
a. x
b. x
c. log(b)X = y
d. 1
e. x
f. 0
g. 1
h. indeterminate (the limit would be infinity)
i. 0 (limit) a is a smallish number
j. oo(limit) a is any smallish number
More general knowledge!
a. sin0
b. cos0
c. tan0
d. sec0
a. 0
b. 1
c. 0
d. 1
What is the derivative of (sr stands for square root):
a. sin^-1x and for cos add a ____
b. tan^-1x and for cot add a ____
c. sec^-1x, and for csc add a ____
d. Remember x is the _________ and remember you still have to apply ________
a. 1/sr(1-x^2), add - for cos
b. 1/1+x^2, add - for cot
c. 1/|x|sr(x^2 -1), add - for csc
d. argument, chain rule
a. int tanx =
b. int cotx =
c. int secx
d. int cscx =
a. ln|secx| + C
b. -ln|csc|+C
c. ln |secx+tanx| + C
d. ln|cscx-cotx| + C
a. derivative of log(b)x =
b. int b^x =
a. 1/xlnb
b. (1/lnb)(b^x) + C
