111H_hw1 (1)

111H_hw1 (1) - Math 111H Problem Set 1 Fall 2012 Read each...

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Math 111H Problem Set 1, Fall 2012 Read each problem carefully. Show all your work for each problem! Use only those methods discussed thus far in class. 1. Given f ( x )= x 2 +4 , Fnd the average rate of change on the interval [-1, 3]. ±ind a point on this interval where the instantaneous rate of change is equal to the average rate of change just found. 2. Evaluate the following limit lim x 2 6 x 2 3 x 1 . 3. ±ind all values of the constant, a, so that f (3) = lim x 3 f ( x ) . f ( x ° x 2 9 x 3 + a, x ° =3 a 2 ,x . 4. ±or the given function, (i) sketch by hand f ( x ) on the interval x [ 2 , 2] , and (ii) evaluate the limits lim x 0 f ( x ) and lim x 1 f ( x ) , if they exist. f ( x | x +1 | 0 x | x | + x, 0 <x 1 3 x, x > 1 . 5. Use MATLAB to plot the functions sin
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