Show:
Derivatives
Implicit Differentiation
Limits
Justifications
100
What is derivative of 2x^2?
4x
100
What is the implicit differentiation of x^3+y^3=1?
dy/dx=x^2/y^2
100
lim (8-3x+12x^2) x>2
50
100
If the acceleration of a particle is positive, then the velocity is ________________________.
Increasing
200
What is the derivative of 2x^4?
8x^3
200
What is the implicit differentiation of x^2+xy-y^2=4?
dy/dx=-2x/(x-y)
200
lim x^2+4x-12 x->2 _________ x^2-2x
4
200
The speed of a particle is decreasing when
Velocity and Acceleration doesn’t have the same sign
300
What is the derivative of (4x^2)(3x)?
36x^2
300
What is the implicit differentiation of 2x^3+x^2y-xy^3=2?
dy/dx=-6x^2-y^3-2xy/(x^2+3xy^2)
300
lim 2(-3+h)^2 - 18 h->0 --------------- h
-12
300
An object is at rest when velocity is _________. 
equal to 0
400
What is the derivative of 5x^2/2x^5?
-30x^6
400
What is the implicit differentiation of x^4(x+y)=y^2(3x-y)?
dy/dx=5x^4+4x^3-3y^2/3x2y-3y^2-x^4
400
lim 100x^6-1231x^3+513x x->oo ------------------------- 500x^2-100000x+25x^6
4
400
A function will have points of inflection when the second derivative
is changing signs and is equal to 0
500
What is the derivative of x^3+5x+3/x^2+1?
x^4-12x^2-6x-5/(x^2-1)^2
500
What is the implicit differentiation of xe^y=x-y?
dy/dx=e^y-1/1-xe^y
500
lim t->4 t- √(3t + 4) ------------- 4-t
-5/8
500
If the velocity of a particle is decreasing, then the acceleration is
Negative