Final Exam Review Session [Part 1]

Approximating Limits

100

Find the following Limit:

lim_(x->1)(x^3+5x^2-7x+1)

Limit = 0

200

Find the following Limit:

lim_(x->-4)sqrt(x^2+2x+1)

Limit = 3

300

Find the following Limit using any Technique, if it exists:

lim_(x->0)(x^3+12x^2-5x)/(5x)

Limit = -1

400

Find the following Limit using any Technique, if it exists:

lim_(x->4)(x^2+4x-32)/(x^2-16)

Limit = 3/2

500

Find the following Limit using any Technique, if it exists:

lim_(x->pi/2)(cosx)/(cotx)

Limit = 1

600

Find the following Limit using any Technique, if it exists:

lim_(x->9)(sqrt(x-5)-2)/(x-9)

Limit = 1/4

Derivatives (Product Rule)

100

Find the First Derivative of:

y=6-x^6cosx

y'=x^6sinx-6x^5cosx

200

Find the First Derivative of:

y=(4x-5)(4x^3-x^2+1)

y'=4(4x^3-x^2+1)+(4x-5)(12x^2-2x)

or

y'=64x^3-72x^2+10x+4

300

Find the First Derivative of:

y=(x^2-4x+2)(5x^3-x^2+4)

y'=(2x-4)(5x^3-x^2+4)+(x^2-4x+2)(15x^2-2x)

or

y'=25x^4-84x^3+42x^2+4x-16

400

Find the Second Derivative of:

y=7xsin x

y''=14cosx-7xsinx

500

Find the First Derivative of:

y=4x^2tanx

y'=8xtanx+4x^2sec^2x

600

Find the First Derivative of:

y=secx tanx

y'=secxtan^2x+sec^3x

Derivatives (Quotient Rule)

100

Find the First Derivative of:

y=x^3/(x-1)

y'=((x-1)(3x^2)-x^3(1))/(x-1)^2

or

y'=(2x^3-3x^2)/(x-1)^2

200

Find the First Derivative of:

y=(3x^2)/sinx

y'=((sinx)(6x)-(3x^2)(cosx))/sin^2x

or

y'=(6xsinx-3x^2cosx)/sin^2x

300

Find the First Derivative of:

y=(x^2+5)/(x^2+6x)

y'=((x^2+6x)(2x)-(x^2+5)(2x+6))/(x^2+6x)^2

or

y'=(6x^2-10x-30)/(x^2+6x)^2

400

Find the First Derivative of:

y=(x^3-2x^2)/ln(x)

y'=((lnx)(3x^2-4x)-(x^3-2x^2)(1/x))/ln^2x

or

y'=(3x^2lnx-4xlnx-x^2+2x)/ln^2x

500

Find the First Derivative of:

y=(x^2-3x+2)/(x^7-2)

y'=((x^7-2)(2x-3)-(x^2-3x+2)(7x^6))/(x^7-2)^2

600

Find the First Derivative of:

y=(3-cos x)/(sin x+x)

y'=((sinx+x)(sinx)-(3-cosx)(cosx+1))/(sinx+x)^2

Derivatives (Chain Rule)

100

Find the First Derivative of:

y=(6x^2-2x+3)^4

y'=4(6x^2-2x+3)^3(12x-2)

200

Find the First Derivative of:

y=sqrt(17x-x^5)

y'=(17-5x^4)/(2sqrt(17x-x^5))

300

Find the First Derivative of:

y=cos^5(3t-8)

y'=-15cos^4(3t-8)sin(3t-8)

400

Find the Second Derivative of:

y=5(2t+3)^3

y''=240t+360

500

Find the First Derivative of:

y=((cosx)/(1+sinx))^5

y'=-5((cosx)/(1+sinx))^4(1/(1+sinx))

600

Find the First Derivative of:

y=tan(cos(3x^2-5))

y'=-6xsec^2(cos(3x^2-5))sin(3x^2-5)

Joker Questions!!

100

What are the SI Leader's names?

David & Javier!

200

What days does Javier lead the SI Sessions??

 Monday & Wednesday!!

300

What transportation method does David use to arrive at class???

A Scooter!!!

400

What's the room number where we usually have the SI Sessions????

Y2-202!!!!

500

What is Javier's Minor?????

Astronomy!!!!!

600

Who's David favorite Superhero??????

Spider-Man!!!!!!