midterm 2 study guide

# midterm 2 study guide - c of f(x)=b then lim...

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Continuity test 1. c lies in the domain of f: f(c) exists 2. f has a limit as x c 3. the limit of f(x)=f(c) Properties of Continuous Functions -if f and g are continuous at x=c, then the following combinations are continuous at x=c 1. sums: f+g 2. differences: f-g 3. products: f x g 4. constant multiples: k x f, for any number k 5. quotients: f/g, provided g(c) !=0 6. powers: f^r/s, provided it is defined on an open inter containing c, where r and s are int Composite of Continuous Function If f is continuous at c and g is continuous at f(c), then the composite of g(f) is continuous at c. Theorem 11 If g is continuous at point b and lim as x
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Unformatted text preview: c of f(x)=b, then lim g(f(x))=g(b)=g(lim(f(x))). This is the epsilon/delta proof, Slope of a curve Lim h 0 of (f(x0+h)-f(x0))/h h is like delta x, the distance between the two points on the line of the graph if its secant. Product Rule f(g) is f’x g+ fx g’ Derivative quotient (Hodhi-hidho)/hoho Darboux’s theorem If a and b are any two points in an interval on which f is differentiable, then f’ takes on every value between f’(a) and f’(b). Instantaneous rate of change is the derivative of the function. Chain Rule f(g(x)) = f’(g(x)) x g’(x)...
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