Green AP Calculus AB

The notation lim_(x→a)f(x)=c means... : As x goes to a, f(x) gets closer and closer to y=c.

f(x) has a horizontal asymptote at y=c if... : lim(x→∞)f(x)=cor lim(x→-∞)f(x)=c

To prove that f(x)is continuous at x=a : Show thatlim(x→a) f(x)=f(a)(use 2-sided limits when necessary)

Intermediate Value Theorem : A function y=f(x) that is continuous on [a,b] takes on every value between f(a) and f(b). If y0 is between f(a) and f(b), then y0=f(c) for some c in [a,b].

Ѳ=30°,π/6 sinѲ=cosѲ=tanѲ= : sinѲ=1/2cosѲ=√3/2tanѲ=1/√3

Ѳ=45°,π/4 sinѲ=cosѲ=tanѲ= : sinѲ=1/√2cosѲ=1/√2tanѲ=1

Ѳ=360°, 2π sinѲ=cosѲ=tanѲ= : sinѲ=0cosѲ=1tanѲ=0

sin(2x)= : 2sinxcosx

1+tan^2x : sec^2x

cot^2x+1 : csc^2x

Given f(x)=c (a constant function)f '(x)= : 0

Given u is an expression in x and f(x)=cu f'(x)=d(cu)/dx= : cu'=c du/dx

d/dx (f ° g)(x)=d f(g(x))/dx= : f^' (g(x)) g^' (x)

Given u is an expression in x and f(x)=e^u f'(x)=d(e^u )/dx= : e^u u'=e^u du/dx

Given u is an expression in x and f(x)=sin(u) f'(x)=d/dx(sinu)= : cos(u)u'=cos(u) du/dx

Given u is an expression in x and f(x)=cot(u) f'(x)=d/dx(cotu)= : (-csc^2)(u) u'= -csc^2(u) du/dx

Given u is an expression in x and f(x)=csc(u) f'(x)=d/dx(cscu)= : -csc(u)cot(u) u'=-csc(u)cot(u)du/dx

Given u is an expression in x and f(x)=arcsec(u)=sec^(-1)(u) f'(x)=d/dx(arcsecu) : 1/(|u|√(u^2-1)) u^'=1/(|u|√(u^2-1)) du/dx

Critical numbers occur at values of x where a) ___________b) ___________ : a) f '(x)=0b) f '(x) is undefined

If f(x) is continuous on [a,b], the Extreme Value Theorem states: : f(x) must have an absolute maximum and an absolute minimum on [a,b].

If f^' (x)<0 on an interval, then f is __________ on the interval. : decreasing

A relative maximum occurs at a critical number c where i)__________________ : i) f '(x) changes from + to -

Given s(t) gives position at time t,s^' (t) gives i)_______〖|s〗^' (t)| gives ii)_____s^''(t) gives iii)______s^'''(t) gives iv)_____ : i) Velocity at time tii) Speed at time tiii) Acceleration at time tiv) Jerk at time t

If a particle is speeding up, its velocity and acceleration have the_____________sign. If a particle is slowing down, its velocity and acceleration have _______________signs. : Same; opposite

∫1/u du = : ln |u|+C

∫sinu du : -cosu+C

∫cotu cscu du : -cscu+C

∫a^u du = : a^u/lna +C

The formula for the area of a trapezoid w/ bases b1, b2 and height h : A= 1/2 (b_1+b_2 )h

The formula for the area of a washer with large radius R and small radius r : A=π(R^2-r^2)