Try the fastest way to create flashcards

AP Calculus Review Notecards

Get a hint
Find the zeros
Click the card to flip 👆
1 / 79
1 / 79
Terms in this set (79)
Find the zeros
aka: find the roots
set function = 0
* factor or use quadratic equation if quadratic
* graph to find 0s on calculator
Image: Find the zeros
Show that f(x) is even
Algebraically: show that f(-x)=f(x)
Graphically: see if symmetric about the y axis
Image: Show that f(x) is even
Show that f(x) is odd
Algebraically: show that f(-x)= -f(x)
Graphically: see if symmetric about the origin
Image: Show that f(x) is odd
Show that lim x→a f(x) exists
Show that lim x→a- f(x) = lim x→a+ f(x)
Image: Show that lim x→a f(x) exists
Find lim x→a f(x), calculator allowed
Find values of the function for x-values close to a from BOTH the left AND the right
Image: Find lim x→a f(x), calculator allowed
Find lim x→a f(x), no calculator
If you can substitute x=a directly in, then do it!

If you cannot substitute x=a in, try to:
* Factor/reduce
* Rationalize radicals
* Simplify complex fractions
* If piecewise, check if limit from the right = limit from the left
* use known trig limits
-- lim x→0 sinx/x = 1
-- lim x→0 (1-cosx)/x = 0
Image: Find lim x→a f(x), no calculator
Find lim x→∞ f(x), calculator allowing
Do Y1(1000000) on your calculator
Image: Find lim x→∞ f(x), calculator allowing
Find lim x→∞ f(x), no calculator
Think:
* small/big = 0
* big/small = DNE
* same/same = ratio of coefficients

same rules apply to x→-∞
Image: Find lim x→∞ f(x), no calculator
Find horizontal asymptotes of f(x)
Find lim x→∞ f(x) and lim x→-∞ f(x)
Image: Find horizontal asymptotes of f(x)
Find vertical asymptotes of f(x)
Find where lim x->a f(x)=±∞
* factor/reduce f(x) and set denominator = 0
* remember ln x has VA at x=0

It's very important that you remember to factor FIRST before setting your denominator = 0. If a factor in the denominator crosses out with a factor in the numerator, then your function has a HOLE there and not a vertical asymptote.
Image: Find vertical asymptotes of f(x)
Find domain of f(x)
Assume domain is (-∞,∞)
Restrictable domains:
*Denominators ≠ 0
*Square roots of only nonnegative numbers
*Log or ln of only positive numbers
*Real world constraints (ie: time≥0)
Image: Find domain of f(x)
Show that f(x) is continuous
Show that 1=2=3:
1. lim x->a⁺ f(x)
2. lim x-> a⁻ f(x)
3. f(a)
Image: Show that f(x) is continuous
Find the slope of the tangent line to f(x) at x=a
Find derivative f '(a) = m
Image: Find the slope of the tangent line to f(x) at x=a
Find equation of the line tangent to f(x) at (a,b)
f '(a) = m and use y-y₁=m(x-x₁) → y-b=m(x-a)
* if they don't give you the point and instead say "find the equation of the line tangent to f(x) at x=a", then we first find the point by computing f(a)
Image: Find equation of the line tangent to f(x) at (a,b)
Find equation of the line normal (perpendicular) to f(x) at (a,b)
m = -1/f '(a) and use y-y₁=m(x-x₁) → y-b=m(x-a)
* if they don't give you the point and instead say "find the equation of the line normal to f(x) at x=a", then we first find the point by computing f(a)
Image: Find equation of the line normal (perpendicular) to f(x) at (a,b)