Limits
Derivatives
Theorems
Function Analysis
Potent Particles
Triple Rhyme Time
100
lim_(x\rightarrow1) (2x^2+x-3)/(x-1)
What is 5?
100
Find the derivative of...
f(x)= xlnx - x
What is
f prime (x) = ln x
100
Give an example of a function that is continuous but not differentiable everywhere
What is |x| ?
100
A function f(x) has the derivative...
fprime(x)=(x+1)(x-2)(x-4)
It's the number of local maximums f has.
What is 1 local maximum?
100
It's the acceleration of the particle at time t= 1 whose position is given by...
x(t)= 2t^3+e^(-4t)
What is...
12+16e^(-4) approx 12.293
100
A frightful creamery pixie
What is a scary dairy fairy?
200
lim_(x\rightarrow3^+) (x-4)/(x^2-9)
What is
-infty
200
Given that...
g(x) =f(x^2)/sinx
Find the derivative of g in terms of f
What is...
gprime(x)=(2xfprime(x^2)sinx-f(x^2)cosx)/sin^2x
200
If f is continuous and f(2) = f(5), what statement(s) are true?
I. f has a critical point on [2, 5]
II. f both increases and decreases on [2, 5]
III. f'(c) = 0 for some c in [2, 5]
What is I only ?
200
It's the minimum value on the interval [0, 3] of...
f(x)=xlnx
What is
f(e^-1)=-e^-1
200
It's the maximum positive velocity of the particle whose position is given by...
x(t)=-2/3x^3+1/2x^2+6x
What is 6.125?
200
Wet-earth smeared pal who's part of your test prep team
What is a muddy study buddy?
300
lim_(x\rightarrow0) (cosx - 1)/x^2
What is -1/2?
300
Find the equation of the tangent line to
y=8xtan(pix)
at x = 1/4
What is...
y-2=(8+4pi)(x-1/4)
300
Find two values of x that prove a solution to the following equation through the Intermediate Value Theorem:
log_3x = cos(pix)
What is x = 1 and x = 3 (as two possible examples)
300
It's intervals in which f(x) is increasing
What is [-2, 1] and [1,3]
300
It's whether the particle whose velocity is given below is speeding up or slowing down at the given time.
v(t)=sin(t) , t = (11pi)/6
What is slowing down?
300
Exploring Hellenic mountains for 7 days
What is a Greek peak week?
400
lim_(x\rightarrow\infty)lnx/sqrtx
What is 0?
400
Find the slope of the line tangent to...
e^(xy)-y^2=e-4
When x = 1/2
What is...
(4e)/(8-e)
400
Which of the following functions can the Mean Value Theorem be applied to on the interval [1, 5] ?
I.
f(x)=(x-2)/|x-2|
II.
f(x)=ln(|x|)
III.
f(x)=|sinx|
What is II only?
400
It's either a relative maximum, relative minimum, neither or indeterminable of a twice differentiable function f(x) at x = -2 that meets the following conditions...
I. f has a relative maximum at x = 2
II. f(-x) = -f(x) for all x
What is a relative minimum?
400
It's the linear approximation for the position of the particle at t = 3.5 if its position at t = 4 is 5 and velocity is given by...
v(t)= t * ln(t)
What is...
5-2ln(4) approx 2.227
400
A searing camp bed scheme
What is a hot cot plot?
500
lim_(xrightarrowinfty) ((2x-1)(x+3)(3x-4)(5x+2))/((2x+5)^4
What is 15/8 ?
500
Find the nth derivative of
y=(x+n)^n
What is n!
500
It's the value of a such that the function f has the MVT satisfied at x = 3 on the interval [0, a].
f(x)=x^2+2x+1
What is a = 6 ?
500
It's the maximum and minimum value on the interval [0, 4] of...
f(x)=sqrtx/(x+1)
What is maximum of (1, 0.5) and minimum of (0, 0)
500
It's the time that particle is farthest to the right on the interval [0, 4] if its initial velocity is 6 and acceleration is given by...
a(t)=2t-7
What is t = 1?
500
A small and portable spacecraft plug receptacle
What is a pocket rocket socket?