Formula Quiz Flashcards
limit from the left of f(x) as x approaches a
lim x-> a- f(x)
limit from the right of f(x) as x approaches a
lim x-> a+ f(x)
0/#
0
/0
undefinded
formal definition of the derivative
lim h-> 0 f(x+h)-f(x)/ h
alternative form of the derivative
lim x-> c f(x)-f(c)/x-c
constant rule
d/dx [c]=0
chain rule
d/dx [f(g(x))]=f’(g)*g’
product rule
d/dx [fg]= f’g+g’*f
quotient rule
d/dx [f/g] = gf’ - fg’/ g^2
where does the limit not exist
Jumps
Oscillation
Infinity
vertical asymptotes
denominator cannot = 0
horizontal asymptotes
look both ways (limit at - infinity and + infinity)
equation of the tangent line
y-y1=m (x-x1)
Limits at infinity B/S
DNE
Limits at infinity S/B
0
Limits at infinity S/S
fraction
d/dx (ln u)
u’/u
d/dx (e^u)
u’ * e^u
d/dx (a^u)
ln (a) * u’ *a^u
inverse funtions of g’(x)
f(x)= function
g(x)= inverse
g’(x)=1/ f’(g(x))
graph y=e^x
graph goes through 1 at the y axis and goes in a curves like up to the right and down to the left (horizontal line)
e^0=
1
graph y=ln(x)
graph goes through 1 on the x axis and goes up to the right and down to the left along the y axis but not touching it
d/dx x^n
nx^n-1
