Answer Key
795
b. ∞. The magnitude of the electric field as you approach the particle q becomes infinite. It does not make physical sense to evaluate negative distance. 131 . The function is defined for all x in the interval (0, ∞). 133 . Removable discontinuity at x =0; infinite discontinuity at x =1
135 . Infinite discontinuity at x = ln2 137 . Infinite discontinuities at x = (2 139 . No. It is a removable discontinuity. 141 . Yes. It is continuous. 143 . Yes. It is continuous.
k +1) π
k =0, ±1, ±2, ±3,…
4 , for
145 . k =−5 147 . k =−1 149 . k = 16 3 151 . Since both s and y = t are continuous everywhere, then h ( t ) = s ( t )− t is continuous everywhere and, in particular, it is continuous over the closed interval ⎡ ⎣ 2, 5 ⎤ ⎦ . Also, h (2) =3>0 and h (5) =−3<0. Therefore, by the IVT, there is a value x = c such that h ( c ) =0. 153 . The function f ( x ) =2 x − x 3 is continuous over the interval ⎡ ⎣ 1.25, 1.375 ⎤ ⎦ and has opposite signs at the endpoints. 155 . a.
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