Logs
Limits
Power / Product / Quotient Rule
Mystery
100
5^x=3
ln(3)/ln(5)
100
lim x->5 (sqrt(x))/(x+1)
sqrt(5)/6
100
State the Product Rule
gf'+fg'
100
sin(pi/3)
sqrt3/2
200
ln(e^x)=5
5
200
lim x->3((x-3)/(x^2-9))
1/6
200
State the quotient rule
(gf'-fg')/g^2
200
arccos(cos(pi/3))
pi/3
300
ln(e^(ln(e^(x^2))))
x^2
300
limx->0((4^(2x)-1)/(4^x-1))
2
300
Find f'(x) without simplifying
f(x)=4x^3+3x^2+2+1
f'(x)=12x^2+6x+2
300
What time is the exam, and how much time will you have to complete it?
9:05 pm - 10:55 pm (80 mins)
400
ln(3x^2)-ln(x)=5
e^5/3
400
lim x->0 (tan(5x)/sec(5x))
0
400
Find f'(x) without simplifying
f(x)=(x^2+3x+5)(3x^2+5x+7)
f'(x)=(x^2+3x+5)(6x+5) + (3x^2+5x+7)(2x+3)
400
What is the limit definition of a derivative? (State one)
500
ln(x)−ln(x^2) + ln(x^3) = 5
e^(5/2)
500
Horizontal and Vertical Asymptotes
f(x)=(4+x)/(3-3x)
Vertical, x=1
Horizontal, y=-1/3
500
Find h'(x) without simplifying
h(x)=(x^3+1)/(sqrtx + 1)
h'(x) = ((sqrtx + 1)(3x^2)-(x^3+1)(x^(-1/2)/2))/(sqrtx+1)^2
500
arcsin(sin((4pi)/3))
-pi/3