Chapter 1.1 Notes - Lauren Nitahara Calculus Notes Chapter...

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Lauren Nitahara Calculus Notes Chapter 1.1 SECANT LINE TANGENT LINE m sec  = f(c+         x) – f(c)     m tan      x * Read examples on pages 66-67 #1-2 Consider f(x) = x    2    – 4     X + 2 x -2.01 -2.001 -2 -1.999 -1.99 f(x) -4.01 -4.001 ? -3.999 -3.99 We’d like  f(-2) = 4 This graph is a straight line that has a gap at point (-2,-4).  Though x -2 we can move arbitrarily  close to -2 from either left or right. So we say here lim f(x) = 4  -2 Def : If f(x) becomes arbitrarily close to a single real number L as x approaches c from either side, the limit  of f(x) as x approaches c is L. Write: lim f(x) = L                x   c Example : Consider h(x) =   4 if x   1      0 if x = 1 Because h(x) = 4, for all x (other than 1) we conclude lim h(x) = 4                 x   1
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Chapter 1.1 Notes - Lauren Nitahara Calculus Notes Chapter...

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