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Unformatted text preview: U nit 1: I n t roduction to Calculus limx →afx=L
• X is a very-very close to but not equal to ‘a’ o Must be a number on each side of a • The limi t of the function only exist if the limit from the left is equal to the limit from t he r ight limx→a-fx=limx→a+f(x) • One sided limits • The limi t of f(x) as x approaches to infinity is 0 Propert ies: 1. limx→ak=k 2. limx→ax=a 3. Lim it of a sum or Difference limx→afx± gx=limx→afx± limx→ag(x) 4. Lim it of a Constant limx→acf(x)=c limx→af(x) 5. Lim it of a product limx→afxg(x)=limx→afx× limx→ag(x) 6. Lim it of a quot ient limx→af(x)g(x)=limx→af(x)limx→ag(x) Note: limx→ag(x)≠0 7. Lim it of a power limx→a[fx]n=[limx→af(x)]n Ex) limx→3x2+2x-6= limx→3x2+limx→32x-limx→36 [limx→3x]2+ 2limx→3x- limx→36  2 + 2-6 9 W hen x →0 divide top & bottom (every term) by highest term Ex) f(x)=x2 if x≤14-1 if x>1
(i). Find limit as x approaches to 1 from the r ight (ii). Find limit as x approaches to 1 from the left • • • • • • • If function is not defined below or above a certain number, i t does not exist F(x) is continuous for every x in the domain if there are no breaks or holes in the g raph o Polynomial functions If there are breaks or holes the function is discontinuous o Discontinuity is described by x-coordinate of point where break occurs Holes and asymptotes occur with rational functions Jump occurs with multi-defined (piecewise) functions The only place where a function (jump) is discontinuous is where the function switch d irections Slope of tangent to y=f(x) -P(a, f(a)) -Q[(a+h),f(a+h)] m = limh→0fa+h-f(a)a+h-a m = limh→0fa+h-f(a)h K nown as First Principles ...
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This note was uploaded on 01/03/2011 for the course CALC 1 taught by Professor George during the Spring '99 term at Western University of Health Sciences.
- Spring '99