Homework_3_Solutions

# We cannot even say that the limit approaches or

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and do not stay close to any fixed real number. We cannot even say that the limit approaches or because when x < 1 , the function 1 x 1 takes on values that are negative; but when x > 1 , the function is positive. So an additional reason that the limit can not exist is that the function does not approach from both the left and right, nor does it approach from both the left and the right.

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Math 1110 (Fall 2011) HW3 Presentation Problems 2 Question 2. (6 points) Suppose that f ( x ) is an even function of x . Does knowing that lim x 2 f ( x ) = 7 tell you anything about either lim x 2 f ( x ) or lim x 2 + f ( x ) ? Give reasons for your answers. Since f is an even function x , we know that for each point c in the domain of f , c is also in the domain of f and f ( c ) = f ( c ) . In particular, this means that if a right-hand limit exists for f as x c , then a left-hand limit exists for f as x c and the two are equal. Similarly, if a left-hand limit exists for f as x c , then a right-hand limit exists for f as x c and the two are equal.
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• Fall '06
• MARTIN,C.
• Calculus, Limit, Continuous function

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