When finding an asymptote of a function where the denominator has a greater exponent than the numerator, the value is…
0
When finding an asymptote of a function where the numerator has a greater exponent than the denominator, the value is…
There is no asymptote
When finding an asymptote of a function where the denominator has an equal exponent to the numerator, the value is…
The ratio of the coefficients of the numbers with the greatest exponent
Another word for ‘Instantaneous rate of change of a function’ is
Derivative / f’(x)
Mean Value Theorem (MVT)
for a function continuous on a closed interval, there must be a point where IROC matches AROC
f’(c) = (f(b)-f (a))/(b-a)
ln(e)=
1
ln =
log base e (x)
when looking for a point of inflection, where should you look for a change in concavity
acceleration – f’‘(x)
inverse f(x)
flip x + y, solve for y, replace y= with f^-1(x)
inverse f’(x)
1 / f’(f^-1(x))
csc(x)=
1/sin(x)
sec(x)=
1/cos(x)
cot(x)=
1/tan(x)
d/dx (tan(x))
sec^2(x)
d/dx (cot(x))
csc^2(x)
d/dx (sec(x))
sec(x) tan (x)
d/dx (csc(x))
csc(x) cot(x)
Intermediate Value Theorem (IVT)
if f(x) is continuous on a closed interval [a,b] and N is any number between f(a) and f(b), there is a value c within [a,b] for which f(c)=N
0s of a function can be
points of inflection OR just regular zeroes
