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Intermediate Value Theorem_Notes

Intermediate Value Theorem_Notes - a(a x = x a loga^x =x...

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Intermediate Value Theorem – if f is continuous on [a,b] and s is btw f(a) and f(b) then there exists a number c in [a,b] such that f( c) = s Mean value theorem – suppose that f is continuous on [a,b] then there exists a c so that f(b) – f(a) / b – a = f `( c) Trig identities – sin 2 x + cos 2 x = 1. sec 2 x = 1 + tan 2 x. csc 2 x = 1 + cot 2 x. sin2x = 2sinxcosx. Cos2x = 2cos 2 x – 1 = 1 – 2sin 2 x. Invesrse function identies –f -1 (f(x))=x. f(f -1 (x))=x. (f -1 ) -1 = f(x) Derivative of an inverse function – d/dx f -1 (x)= 1/(f˙(f -1 (x)) Log/ln/e identities – log
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Unformatted text preview: a (a x) = x. a loga^x =x. log s x = log b x/log b a. lnx = log e x. a x =e xlna . d/dx a x = d/dx e xlna = e xlna lna = a x lna. d/dx log a x = 1/xlna Error equation = next step in linearization: (F''(s)/2)(x-a) 2 1) Choose the interval that will maximize your F''(s) as your s in order to get K. abs(F''(s)) < K (maximum). If increasing concave up underestimate intervals are (estimate, estimate + error). 9). If decresing concave down overestimate intervals are (estimate – error, estimate)...
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