Unlimited Fun
The limit of f(x) as x approaches 3
f(x)=((3x - 2x^2))/(7x)
What is:
-3/7
The derivative of
f(x)=sin(pi x)
f'(x)=picos(pi x)
How many students are in our class at full capacity?
20
When f' changes from negative to positive, f will have a __________
10
10x
The limit of f(x) as x approaches infinity
f(x)=(2x^4)/(3x^3-1)
Infinity
Find f''(1/2)
f(x)=(2x^4)
6
How would an engineer estimate the gravitation constant in m/s^2?
10
In a concave __ function, a Left Riemann Sum will be an overestimate of area.
Up
x^2
x^3/3
f(x)=(x^2-4)^(1/3
f'(x)=(2x)/(3(x^2-4)^(2/3)
This is the student with the fewest total letters in their name
Leo Sohn
In a concave down function, a linear approximation will be an _______________ of the value of the function.
Overestimate
cos(2x)
1/2sin(2x)
Find dy/dx.
xy=sin(cos(x))-3pi
dy/dx=(-cos(cos(x))sin(x)-y)/x
Total students in this class that Zev teaches their sibling.
6
If f'(1)=2 and f''(1)=-2, then at x=1 the original function will be ________ (increasing/decreasing) and concave ____ .
Increasing and Concave Down
1/2x^(-1/2)
sqrt(x)
The limit of f(x) as x approaches 0
f(x)=((1/(x-4))+(1/4))/x
-1/16
Find dy/dx
cos(xy)=4x+4
(-4/sin(xy)-y)/(x)
(Teams in color war)^(total hyphenated last names in this class)-(Students with a last initial of V)
62
State how you can identify the difference between a cusp and vertical tangent line just by examining the derivative of the function
Cusp: the limit of the derivative will approach opposite infinities
Vertical Tangent Line: the limit of the derivative will approach the same infinity
8x(x^2+5)
2(x^2+5)^2