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Unformatted text preview: -0.1 0.99837 0.01 0.99998-0.01 0.99998 0.001 0.999998-0.001 0.99999833 Definition of limit: Assume f(x) is defined for all x near c. but not necessarily at c. its e(t) we say the limit of f(x) as x approach c is equal to L. If f(x)-4 becomes arbitrarily small when x is any number sufficiently close to c (not equal) We write: Lim f(x) =L We say f(x) converges to L as x ->c Ex. Lim (x-:>2) 2x+3 = 7 Absolute value of f(x) L = absolute value of 2x+3 -7 = absolute value of 2x-4 = 2 times the absolute value of x-2 Since absolute value of f(x) L is a multiple of the absolute value of x-2, Absolute value of f(x) L become arbitrary small as x is close to 2. Theorem a) lim x->2 k=k b) lim x->c x= c ex. Lim x->0 e ^(-1/x^2) = 0 x F(x) + 1 e ^-1 +0.1 e ^-100 +0.01 Example 1 (limit equals function value) F(x)= x Lim (x->4) x = 2...
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