dA/dt of the area of a triangle with base= b and height = h
What is 1/2(b dh/dt + h db/dt)?
100
The limit as x approaches 2 for f(x) = (x^2 - 4)/(x - 2)
What is 4?
100
Factor x^2 - 7x + 12 and find the roots
What are -4 and -3?
200
dy/dx of x^2 - y^2 = 16
What is x/y?
200
df(x)/dx of f(x) = (x^3 + 9)^5,
What is 15x^2 (x^3+9)^4?
200
dr/dt for the area of a circle of radius r.
What is [1/(2pi r)] dA/dt?
200
The vertical asymptotes of f(x) = 1/(x^2 - x -6)
What are x = 3 and x = -2
200
The relationship between continuity and differentiability.
What is that continuity does not always imply differentiability , but differentiability always continuity.
300
dy/dx of (x + y)^2 = xy
What is -(2x + y)/(x + 2y)
300
***********DAILY DOUBLE! ******
dy/dx of y = 8 [sqrt(3 -x^4)]
What is (-16x^3)/sqrt(3 - x^4) ?
300
dr/dt of a sphere with Volume = (4/3)(pi r^3) with rate of volume changing at 12 cm/min and radius = 3 cm
What is 1/(3 pi ) ?
300
The both sided limit and the type of this function f(x) such that f(x) = 3x - 2 for x <2 and f(x) =x^2 for x greater than or equal to 2.
What is 4 and piecewise function ?
300
The limit as x approaches zero of f(x)= (sin x/3)/x
What is 1/3?
400
DAILY DOUBLE!!!!! dy/dx of y^2 = sinx cos y
What is (cos x cos y)/(2y + sin x sin y)
400
Given h(x) = 16 x^(1/2) (cos x), find dh(x)/dx
What is -8(2x sin x - cos x)/x^(1/2) or
What is 8(-2 x sin x + cos x)/x^(1/2)
400
The rate of change of the volume (V) wrt time of a cylinder where V=pi r^2 h, with radius r and height h
What is dV/dt = pi [r^2 dh/dt + 2r h (dr/dt) ]?
400
DAILY DOUBLE!
The 3 conditions of continuity at a point "c".
What are f(c) is defined, the both sided limit as x approaches c exists, and that the limit is equal to f(c)?
400
The limit as x approaches infinity of
f(x) =( 8x^4- 3x)/(20x^4 - x^3 + 3x - 1)
What is 4/5?
500
df(x)/dx of f(x) = (-4x)/(5x^2 + 2)
What is 4(5x^2 - 2)/(5x^2 + 2)^2?
500
df(x)/dx of f(x) = (-4x)/(5x^2 + 2)
What is 4(5x^2 - 2)/(5x^2 + 2)^2?
500
The rate of change of the radius of a sphere with surface area (S) = 4 pi r^2, given that the radius is 3 cm and the change in surface area wrt time = 12 cm/min.
What is is 1/(2 pi) ?
500
A list of least 4 types of discontinuities.
What are jump, mixed, endpoint, infinite, removable, oscillating discontinuities?