Derivatives
A derivative is
The slope of the graph at a single point
lim 8x
x --> 2
Plug in 2 for x
16
Definition of an integral
What is a function of which given function is a derivative or what is the area under a curve
Name one of the two calculus inventors
What is Isaac Newton or Gottfried Wilhelm Leibniz
What country has the capital Ulaanbataar
What is Mongolia
The derivative of (6x^2+6)^4
What is 48x(6x^2+6)^3?
4(6x^2+6)^3 Power rule
48x(6x^2+6)^3 Chain rule
48x(6x^2+6)^3
lim (4x+1)/(x-2)
x --> 1
Plug in 1 for all values of x
(4(1)+1)/-1
-5
What is the integral of x² + 3x
What is ⅓x³ +1.5x² + C
What does "Calculus" mean in Latin
What is Pebble/Small Pebble
Who is the Calc BC teacher?
What is Stutz
The derivative of 3x^2+6x+5
What is 6x+6?
3x^2+6x+5 Power Rule
6x+6
Lim (4x^2-4)/ln(x)
x --> 1
8
Plug in 1 for all values of x to find limit
(4(1)^2-4)/ln(1)
0/0
Use L'Hospitals rule for indeterminate. Take derivative of top and bottom
8x/(1/x) --> 8x^2 --> 8
What is the integral of Sin(3x) + 3x³ln(3) + 2xex²
What is -⅓cos(3x) + 9ln(3)x² + ex² + C
What is the derivative of acceleration called (starts with a J)?
What is Jerk?
A technique used for when you have some kind of x raised to the power of some kind of x.
What is logarithmic differentiation?
A useful way for finding the limit of something when it's indeterminate.
What is L'hospitals rule?
Solve 31∫(sec2(x)-30x)dx
What is 2tan(2x)-120x
The best calculus teacher
Who is Ms. Hommowun?
Consider the position of a particle moving along the x-axis given by the function x(t)=3t^4−8t^3+6t^2−2t, where t represents time in seconds. Is the velocity increasing or decreasing at the point x=2.
What is velocity increasing?
v(t)=d/dt(x(t))
d/dt(3t^4-8t^3+6t^2-2t)=12t^3-24t^2-12t-2
v(t)=12t^3-24t^2+12t-2
v(2)=12(3)^3-24(2)^2+12(2)-2
v(2)=22
a(t)=d/dt(v(t))
a(t)=36t^2-48t+12
a(2)=36(2)^2-48(2)+12
a(2)=60
Thus it is increasing.
A limit is
what value the graph looks like it's approaching given an input.
The Fundamental theorem of calculus is used for
Evaluating definite integrals.
Ms Hommowun's favorite candy
What is almond joy?