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# p1812tut01 - 2-16 x 1 has a slope of 5 at exactly two...

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School of Mathematics and Statistics The University of Sydney PHAR1812 Calculus Tutorial 1 1. Round oﬀ each of the following to three signiﬁcant ﬁgures, giving your answer in scientiﬁc notation: ( i ) 3.7142 ( ii ) 0.003817 ( iii ) 12.00 ( iv ) 4.0032 ( v ) 92.65 ( vi ) 7894.0 ( vii ) 1237 ( viii ) 10452.2 2. An experiment resulted in readings of 253 . 71 units and 7 . 251 units. Calculate the sum and the product of these readings, rounding oﬀ your answers suitably. 3. Revision of diﬀerentiation — see Hughes-Hallett Chapter 4 Diﬀerentiate the following (with respect to x ) ( i ) y = x 4 / 3 ( ii ) y = x - 3 / 4 ( iii ) y = e x +5 ( iv ) y = (ln 4) e x ( v ) y = xe x ( vi ) y = x 2 + 5 x + 2 x + 3 ( vii ) y = ( x + 1) 99 ( viii ) y = xe - x 2 4. [More revision] Diﬀerentiate the following (with respect to t ). [The arguments for trigonometric functions are always in radians.] ( i ) y = tan t ( ii ) y = e cos t ( iii ) y = e t cos 3 t ( iv ) y = ln ( cos(1 - t 2 ) ) 5. The graph of the equation y = x 3 - 9 x

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Unformatted text preview: 2-16 x + 1 has a slope of 5 at exactly two points. Find the coordinates of the points. 6. Consider the function f ( x ) = e sin x . Without plotting points, sketch the graph of this function by ﬁguring out some of its properties. Is it periodic? Does it grow unboundedly like an exponential function? Does it ever take a negative value? Does it have any zeros? Does it have a maximum value? A minimum value? 7. ( i ) Show that the relative error for 1 m is approximately the same as that for m . ( ii ) Show that division of measurements causes relative errors to accumulate additively. [Hint: use part (i) and the fact that the multiplication of measurements causes the relative errors to be added.]...
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p1812tut01 - 2-16 x 1 has a slope of 5 at exactly two...

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