Question: A student writes the following: Problem: Evaluate the limit lim V4x+1-3 - 2 x-2 Student answer: Line 1: Direct Substitution is not possible because the

 A student writes the following: Problem: Evaluate the limit lim V4x+1-3

A student writes the following: Problem: Evaluate the limit lim V4x+1-3 - 2 x-2 Student answer: Line 1: Direct Substitution is not possible because the denominator is O when x = 2 . Line 2: Instead let's multiply by the conjugate (to rationalize). Line 3: lim V4x+1-3 -+2 x-2 = lim (V4x+ 1-3) (V4x+1+3) = x-2 x-2 Line 4: = lim (4x+1)-9 x-2 x-2 Line 5: = lim 4(x-2) -2 x-2 Line 6: = lim 4 = 4 -2 Is the student's work correct? (Write "yes" or "no".) If incorrect, in what line is the first error? (Write 1, 2, 3, 4, 5, or 6. If it is correct, write "none". If there is more than one error, write the line of the FIRST error.) The correct final answer to the problem is

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