Exam 1

Logs

100

5^x=3

ln(3)/ln(5)

200

ln(e^x)=5

5

300

ln(e^(ln(e^(x^2))))

x^2

400

ln(3x^2)-ln(x)=5

e^5/3

500

ln(x)−ln(x^2) + ln(x^3) = 5

e^(5/2)

Limits

100

lim x->5 (sqrt(x))/(x+1)

sqrt(5)/6

200

lim x->3((x-3)/(x^2-9))

1/6

300

limx->0((4^(2x)-1)/(4^x-1))

2

400

lim x->0 (tan(5x)/sec(5x))

0

500

Horizontal and Vertical Asymptotes

f(x)=(4+x)/(3-3x)

Vertical, x=1

Horizontal, y=-1/3

Power / Product / Quotient Rule

100

State the Product Rule

gf'+fg'

200

State the quotient rule

(gf'-fg')/g^2

300

Find f'(x) without simplifying

f(x)=4x^3+3x^2+2+1

f'(x)=12x^2+6x+2

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)

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

Mystery

100

sin(pi/3)

sqrt3/2

200

arccos(cos(pi/3))

pi/3

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

What is the limit definition of a derivative? (State one)

500

arcsin(sin((4pi)/3))

-pi/3