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Universities » San Jose State University (SJSU).. » MATH - Mathematics » 30W - Calculus I Workshop » Flash Cards

Calculus AB - Flashcards

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Class:MATH 30W - Calculus I Workshop
Subject:Mathematics
University:San Jose State University
Term:Spring 2011
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 Differentiation of Quadratic Functions:
   If f(x)=ax^2+bx+c, then f '(x)= 2ax+b, so the tangent line is the only coordinate point that is touching one side of the graph. f '(x) =(x,y)
Idea of the Limit:
    Lets say that the number L is the limit of F(x) as x approaches a provided that we can make the number F(x) as close to L as we please merely by choosing x sufficiently near, though not equal to the number a.
Properties of the Limit:
  addition: all real
   multiplication: all real
   division: whether if it defined
   composite: if it is a rational number.
    square root: not negative number
Right and Left hand rule of limits:
   Suppose that f defined on the open interval (a,c) if and if only the coordinate is relatively positive or greater than zero.
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One-sided limit::
if the function f(x) on a neighborhood of the point a. Then the limit f(x) exists and is equal to the number L if and only if the limits are equal to L.
ex 1)
 Lets say the car 1 travels of a maximum speed of 2 seconds at 11 mph, and the speed intersects at a common point when car 2 traveled at a coincident time. So, differentiation applies to physics as the vehicle intersects at a similar speed and time when car 1 has traveled at a certain amount of distance.  The differentiation tells us that slope represented the "total" amount of distance and time for (x,y)=(d,t).
Multiplication rule of derivatives:
 normal distributive property rules applies.
quotient rule:
  bottom to top divided by the square of the bottom number.
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power rule:
 multiply and power down of the exponent  f '(x)= nx^n-1
chain rule:
  differentiate "u" of (dy/dx)*(dx/du) then multiply together as a product.
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   Differentiation of Quadratic Functions:
   If f(x)=ax^2+bx+c, then f '(x)= 2ax+b, so the tangent line is the only coordinate point that is touching one side of the graph. f '(x) =(x,y)

  Idea of the Limit:
    Lets say that the number L is the limit of F(x) as x approaches a provided that we can make the number F(x) as close to L as we please merely by choosing x sufficiently near, though not equal to the number a.
  Properties of the Limit:
  addition: all real
   multiplication: all real
   division: whether if it defined
   composite: if it is a rational number.
    square root: not negative number
  Right and Left hand rule of limits:
   Suppose that f defined on the open interval (a,c) if and if only the coordinate is relatively positive or greater than zero.
  One-sided limit::
if the function f(x) on a neighborhood of the point a. Then the limit f(x) exists and is equal to the number L if and only if the limits are equal to L.
  ex 1)
 Lets say the car 1 travels of a maximum speed of 2 seconds at 11 mph, and the speed intersects at a common point when car 2 traveled at a coincident time. So, differentiation applies to physics as the vehicle intersects at a similar speed and time when car 1 has traveled at a certain amount of distance.  The differentiation tells us that slope represented the "total" amount of distance and time for (x,y)=(d,t).
  Multiplication rule of derivatives:
 normal distributive property rules applies.
  quotient rule:
  bottom to top divided by the square of the bottom number.
  power rule:
 multiply and power down of the exponent  f '(x)= nx^n-1
  chain rule:
  differentiate "u" of (dy/dx)*(dx/du) then multiply together as a product.
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