math21wa2b - Therefore, we know that ( ) h x will never be...

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limx 0+h(x)=0 2) For the function, = ( / ) hx x3cos 1 x , limit law four does not apply as x approaches zero because there cannot be a zero in the denominator of ( / ) cos 1 x . The squeeze theorem can be used to prove that the limit of the function is equal to zero. The squeeze theorem states that if ( ) h x is between ( ) f x and ( ) g x , and → + ( ) limx 0 f x and → + ( ) limx 0 g x are equal, then → + ( ) limx 0 h x is equal to → + ( ) limx 0 f x and → + ( ) limx 0 g x . We know that the cosine of any value is never more than one and never less than negative one.
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Unformatted text preview: Therefore, we know that ( ) h x will never be greater than x cubed and never be less than negative x cubed. So, we can say: = fx x3 and =-gx x3 . We can then calculate the limits of ( ) f x and ( ) g x as x approaches zero from the right. These limits are very simple and we can quickly conclude that → + ( )= limx 0 f x and → + ( )= limx 0 g x . Therefore, according to the squeeze theorem, we can state that → + ( )= limx 0 h x . = ( / ) hx x3cos 1 x = fx x3 limx 0+ → ( )= f x =-gx x3 → + ( )= limx 0 g x...
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This note was uploaded on 11/16/2009 for the course MATH 021 taught by Professor Muralee during the Spring '08 term at Lehigh University .

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