Limits & Continuity
What are the 3 rules to determine if something is continuous?
1) Function value must exist
2) Limit must exist
3) Function value must equal the limit
whats the formula for the quotient rule
u'v-uv' / v^2
Draw me the fun box and describe the meaning
F U N
F' up down
F'' + -
What does math 9 do on your calculator?
It helps you solve antiderivative equations.
Why don't Calculus majors throw house parties?
Because you should never drink and derive.
True or False. If a function f is not defined at x = a then the limit
lim f(x) as x approaches a
never exists.
False. lim f(x) as x approaches a may exist even if function f is undefined at x = a.
The derivative is also known as the what?
Slope!
Whats the MVT?
A theorem that states that if F is continuous and Differentiable, then the AROC=IROC
What is a Riemann sum and what are the different equations used for it?
It is an estimation of the area under the curve.
left sum, right sum, midpoint sum, and trapezoidal sum.
What do you call a wizard who is good at calculus?
A mathemagician
True or False. The graph of a rational function may cross its vertical asymptote.
False. Vertical asymptotes are defined at x values that make the denominator of the rational function equal to 0 and therefore the function is undefined at these values.
what's the derivative of x^5 + 3x^2 - 2x + 7
5x^4 + 6x - 2
If f'(x) is positive, then F(x) is what?
increasing!
what is the antiderivative of 1/x?
ln|x|
Who Made the first circular Table
Sir Cumferance
define a jump discontinuity
Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal.
(lim from left= x and lim from right = y)
If f(x)= 2xcos(x), the f'(0)= ?
0
If F'(x) changes from negative to positive, then F(x) has what?
A relative minimum at that point.
What is the antiderivative of sec^2x?
Tan x
What’s the official animal of Pi day?
The Pi-thon
define a removable discontinuity
a removable discontinuity is one at which the limit of the function exists but does not equal the value of the function at that point
(lim = x & f(x)= y)
What's the derivative of cot?
-csc^2x
If F''(x) is negative and F'(x) is decreasing, then F'(x) is what?
It is concave down.
what is the antiderivitive of x^-7?
-1 / 6x^6 + C
What’s a math teacher’s favorite season?
SUMmer