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Unformatted text preview: Trigonometric Inverse Trigonometric Exponential Logarithmic 9 Where is g ( x ) = x1 + x3 x 2 continuous? If f is continuous at b and lim x c g ( x ) = b , then lim x c f ( g ( x )) = If g is continuous at a and f is continuous at g ( a ), then ( f g )( x ) is continuous at a . i.e. 10 Discuss the limits based on continuity of the functions. lim x e x 2 +3 x1 lim x 2 cos( xcos( x )) 11 An important property of continuous functions is the Intermediate Value Theorem. Suppose f is continuous on [ a,b ] and N is any number between f ( a ) and f ( b ), then 12 Use the IMVT to prove that f ( x ) = x 3 + 3 x2 has a zero in [1 , 1]. 13 Discuss the continuity of f ( x ) = 5x x > 1 x 2 + 1 x 1 14...
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 Calculus, Continuity

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