Limits 1
Limit 2
Derivative Rules
Derivative Applications
Applied Optimization
100
This is:
lim_(xto infty) e^x
What is 0?
100
This is
lim_(t to infty) t^2-t
What is
infty
100
The derivative of g(x)
g(x) = x^6-3sqrt(x)-1
What is
g'(x) = 6x^5-3/(2sqrtx)
100
All the critical points of f(x)
f(x) = x^2-4x+1
What is x=2?
200
This is:
lim_(x to -1) (x^2-1)/(x+1)
What is -2?
200
This is f'(x)
f(x) = x^3(e^x+1)
What is
f'(x) = 3x^2(e^x+1) + x^3e^x
200
The linear approximation of sqrt26 .
What is 5.1?
300
This is
lim_(xto 3) (sqrtx - sqrt3)/(x-3)
What is
1/(2sqrt3)
300
This is
lim_(yto infty) (y^2+4y-10)/(sqrt(9y^4+17y^3-y^2+5))
What is
1/3
300
The d/dx f(x)
f(x) = sin(cos(sin(x)))
What is
f'(x) = cos(cos(sin(x)))*(-sin(sin(x))*cos(x)
300
f(x)'s critical points and interval of increasing/decreasing.
f(x) = 3x^4+8x^3-6x^2-24x
What is x=-2, -1, 1?
Increasing on (-2,-1)cup(1,infty)
Decreasing on (-infty,-2)cup(-1,1)
300
The minimum of two number, whose difference is 100.
What is 50 and -50.
400
This is
lim_(x to 0 ) sin(2x)/tan(3x)
What is 2/3 ?
400
This is:
lim_(x to 0) x^2 cos(1/x)
What is 0?
400
Ethan cycled a 22-mile trail in 78 minutes. His speedometer never read above 15 miles per hour.
The reason why his speedometer is incorrect.
What is Ethan's average velocity at 16.92 mph. He must have reached this instantaneous speed at some point.
400
A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a river with a straight bank. They need no fence along the river.
The dimensions of the field that has the largest area.
What is 1200 ft x 600 ft?
500
This is
lim_(t to infty) (1+pi 3^t)/(4-e^(t+1))
What is -infty
500
This is
lim_(x to 0 ) [1/sinx - 1/x]
What is 0
500
This is dy/dx
xsiny-ycosx=2
What is
dy/dx = (-ysinx-siny)/(xcosy-cosx)
500
The complete analysis of the function f(x). Including:
1) All asymptotes
2) Critical points and intervals of increase/decrease
3) Concavity and inflection points
4) Rough sketch of the function.
f(x)= (3x)/(x^2-1)
V asymptote x=+1, -1
H asymptote y=0
There's no critical points
The function is decreasing over the entire domain except for the vertical asymptotes.
There's a inflection point at x=0.
Concave up (-1,0)cup(1,infty)
Concave down (-infty,-1)cup(0,1)
500
A landscape architect wishes to enclose a rectangular garden of area 1000 m2 on one side by a brick wall costing $90/m and on the other three sides by a metal fence costing $30/m.
The dimensions minimize the total cost.
What is 22.36 m x 44.72 m?