Vocab
What does L'Hospital's Rule state?
If lim as x-->c of f(x)/g(x) produces indeterminates form and if lim as x-->c of f'(x)/g'(x)=L then lim as x-->c of f(x)/g(x)=L
What is the velocity if the position function is s(t)=12x^2-3x
24x-3
What is the derivative of sinx?
Cosx
Name the non removable discontinuities
Infinite(VA) and Jump
What must be to be considered differentiable?
What does the squeeze theorem state?
If f(x) less than or equal to g(x) which is less than or equal to h(x) for x near a, except possibly a, and lim f(x) = lim as x-->a h(x)=L, then lim as x-->a g(x)=L
What are 3 ways to say the derivative of?
f'(x), dy/dx, y'(x), etc.
What is the derivative of cosx?
-sinx
Name the removable discontinuity
Hole
What is the product rule?
h(x)= f(x)g(x)
h'(x)= g(x) X f'(x) + f'(x) X g(x)
What does IVT stand for?
Intermediate Value Theorem
What the derivative of 5x^3 + 7x^2 - 4?
15x^2 + 14x
What is the derivative of e^x?
What is the derivative of position?
Velocity
What is the quotient rule?
h(x)= f(x)/g(x)
h'(x)= (g(x) X f'(x) - f'(x) X g(x))/ (g(x))^2
What does MVT stand for?
Mean Value Theorem
Find the ICRU of the following:
At t=4 seconds, the number of people at a game is increasing at a rate of 5 people per second.
Instant: 4 seconds
Context: Number of people at a game
Rate: Increasing
Units: 5 people per second
What is the derivative of lnx?
1/x
What is the derivative of velocity?
How do you do Chain Rule?
H(x)=f(g(x))
H'(x) = f'(g(x)) X g'(x)
What does EVT stand for?
Extreme Value Theorem
What's the derivative of secx?
secxtanx
sec^2x
How do you determine if a particle is moving left or right?
What is the tangent line equation?
y-f(x)=f'(x)(x-a)