MCV4U Review

Zeros

100

f(x)=2x²+3x+1

x = -0.5, x = -1

200

g(x)=(x+1)e^2x

x = -1

300

F(x)= (x³-4x) / (x²-1)

x = 0, x = -2, x = +2

400

t(x) = x*sqrt(x^2-1)

x <=1, x>=1

500

h(x) = sin(x) + cos(x)   on [0, 2pi]

x = 3pi/4, x = 7pi/4

Turning Points

100

f(x)= (x³)/3+2x²+3x-6

f'(x)=x²-4x+3

(-3,-6) and (-1,-7.33)

200

g(x)=(x+1)e^2x

g'(x)=e^2x(3+2x)

(-1.5,-0.025)

300

h(x)=cos²x      on [0, 2pi]

h'(x)=-2cosxsinx

(0, 1), (pi/2, 0), (pi, 1), (3pi/2, 0), (2pi, 1)

400

f(x)=x³ + x² - x + 2

(-1,3), (1/3, 1.82)

500

f(x)= (x²+4)/(x²-4)

(0,-1)

Inflection

100

f(x)=e^x

There are no inflection points

200

f(x) = x / (x+1)²

f(x) = 2(x-2) / (x+1)⁴

(2, 2/9)

300

f(x) = 2sin(2x)     on [0, pi]

f'(x) = 4cos(2x)

f"(x) = -8sin(2x)

(0,0), (pi/2,0), (pi,0)

400

f(x) = x³ -3x² +7

(1,5)

500

f(x) = xe^x

f'(x) = e^x(1+x)

(-2, -0.27)

Limits

100

Lim f(x) as x->0

f(x)= e^x +4

4

200

Lim f(x) as x->1

f(x)=(x^2+2x-3)/(x-1)

4

300

Lim f(x) as x->3

f(x)=sqrt(x^2-9)/(x-3)

6

400

Lim f(x) as x->1

f(x)=x^2-1,  if x<1

f(x)=x^2+1,  if x>1

DNE

500

Lim f(x) as x->0

f(x)=(cosx)(e^x)(tanx)

1

Mr. Hijab

100

Where is Mr. Hijab originally from?  

Lebanon

200

Favorite sport? 

Basketball 

300

Daughter's name

Zeina

400

Favorite course to teach? 

MCR3UP

500

Name of university? Three, list two: 

Beirut, Sunderland, Waterloo