10Abass - MATH 10A Bonus Assignment (Section B0 ) Name Due...

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MATH 10A Bonus Assignment Name (Section B0 ) Due February 9, 3:50pm in class. This assignment is worth up to 3 points on your Midterm 1 score. You may get help with these problems, but the solution should be written by you in your own words. Ex- plain your solution clearly. You are encouraged to use the midterm solutions as a guide. Problem 1: Find k so that the function f ( x ) = ( x + k, x 5 kx, 5 < x is continuous on any interval. Solution: Each piece of f is continuous. To make f continuous on any interval, we need in particular, to make the left and right hand limits agree at x = 5, and actually be equal to f (5). So we must solve 5 + k = f (5) = lim x 5 + f ( x ) = lim x 5 + kx = 5 k, which gives k = 5 4 . Problem 2: For the function f ( x ) = | 2 x - 6 | x - 3 , find lim x 3 + f ( x ) , lim x 3 - f ( x ) , and lim x 3 f ( x ) . Solution 1 (the graphical way): To obtain the graph of f ( x ), start with | x | x , translate it 3 units to the right, and stretch it vertically by a factor of 2 to get
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10Abass - MATH 10A Bonus Assignment (Section B0 ) Name Due...

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