Differential Calculus Flashcards
Calculus was derived from the Latin Word “Calx” and Greek Word “Chalis” meaning
Calx - Stone
Chalis - Limestone
Mindblown
Founders of Calculus
Gottfried Wilhelm von Leibniz
Isaac Newton
Theorem of Limits
Cal Tech:
instead of using the exact values, use a value approximately equal to the limit
Input Equation
CALC
limit +/- 1x10^-5
Continuity
Cal Tech:
instead of using the exact values, use a value approximately equal to the limit, (one at higher end and one at lower end) and compare if equal
Input Equation
CALC
limit + 1x10^-5
compare to:
Input Equation
CALC
limit - 1x10^-5
if equal then it is continuous
Explicit Derivatives
Cal Tech
L’Hospitals Rule
If Limit of f(x)/g(x) is Indeterminate
then try f’(x)/g’(x)
Maxima/Minima
Cal Tech
Mode Table
Form an equation describing the problem then input limits and increments in the Table Mode to determine the maximum or minimum values from the table’s output column
Change in Concavity
Inflection Point
Largest Rectangle inscribed in a circle
A square with diagonal equal to the diameter
Largest Rectangle inscribed in a semicircle
A rectangle with length equal to the twice the width
Largest Rectangle inscribed in a isosceles / right triangle with corner at the 90 degree corner of the rght triangle
A rectangle with length equal to half the base and width equal to half the height
Largest Rectangle inscribed in an ellipse
A rectangle with base and height equal to sqrt(2) of the semi-major and semi-minor axis of the ellipse respectively
Largest area of triangle w/ given perimeter
Equilateral Triangle
Minimum perimeter of sector given area
r = sqrt(A)
θ=2rad
Rectangle with given area with minimum perimeter
square
