calculus 12- Emma and Tommy

limits

100

lim     (9-x)/(3-x^1/2)

x → 9

what is 6

200

lim        (e^x-2-1)/(x-2)

x→2

what is 1

300

lim     [(1/(x-1))-1]/(x-2)

x→2

what is -1

400

lim     (x⁴-16)/(x-2)

x→2

what is 32

500

lim       (a³-a)/(a-1)

a→1

what is 1

derivatives

100

take the derivative of 

y=4x⁴ +3x³ +7x² +5x +21

what is y'=16x³ +9x² +14x +5

200

take the derivative of y=(sinx)(sin4x)

what is y'=(cosx)(sin4x)+4(sinx)(cos4x)

300

take the 8th derivative of y=sinx

y^viii=sinx

400

find the min/ max of y= 6x² +30x+35 using the derivative

what is (-2.5,-2.5)

500

find y' for x² +xy+y²=490

what is y'= (-2x-y)/(x+2y)

applications

100

Nick Li is driving at a rate of 140km/h, due west. Mr. Easton is driving at a rate of 30km/h due north. When Mr. Easton is 4 km from point a and Nick is 3 km from point a, what is the rate of change of the distance between the two of them?

what is 108km/h

200

find dy/dt for the function y=x³-4x when x=1 and dx/dt is 5

what is dy/dt is -5

300

lim     (x-2)/(x²-4)      using l'Hopital's rule

x → 2

what is 1/4

400

find the line of tangent at the point (3,3) for the function x³+y³=6xy. 

what is x+y-6=0

500

name all the types of critical points. 

what is cusp, corner, infinite tangent, max, min,(discontinuous-P.O.D, Vertical asymptote, jump, end point.)

random

100

(667)(96)

what is 64032

200

894/6

what is 149

300

solve 896x15-6x18

what is 13332

400

a+a=6

a+b=8

3b+c=21

what is c?

what is 6

500

name Mr. Easton's favourite hockey team. 

what is Calgary flames

integrals

100

y'=2x-1

what is y= x²-x+C

200

y'=(4x)⁹

what is y=1/40(4x)¹⁰+c

300

y'=2/x

what is y=2lnx+C

400

find the velocity equation using the equation a=2t+15

what is v=t²+15t+C

500

y'=sin(3x)+x²

y=(1/3)cos(3x)+(1/3)x³