It is known that has limit L = 2 as x approaches 0. Are the following statements

Question

It is known that has limit L = 2 as x approaches 0. Are the following statements about F (x) and L TRUE or FALSE? (Circle one.) The limit of F(x) is exactly L = 2.............................. TRUE FALSE The limit of F(x) is not exactly 2, but is arbitrarily close to L = 2.......... TRUE FALSE F(0) is equal to 2............................. TRUE FALSE The function values F(x) can be made to be arbitrarily close to L = 2..... TRUE FALSE Defining F(0) to be 2 makes the function be continuous at x = 0............. TRUE FALSE

Explanation / Answer

cos(2x) = 1 - 2sin2(x) F(x) = 2sin2(x)/x2 limit x-->0 sin2(x)/x2--->1 => limit x-->0 F(x) = 2

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