workshop3

# workshop3 - Workshop 3 1) Suppose f is deﬁned by f (x) =...

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Unformatted text preview: Workshop 3 1) Suppose f is deﬁned by f (x) = 3ecos x . Maple produced graphs of f and its ﬁrst four derivatives on the interval [2, 7] (be careful when examining the derivative graphs look carefully at the vertical !). The graph of f is to the right, and the graphs of the ﬁrst four derivatives of f are on the back of this page. You should assume that the graphs are correct for this problem. Suppose I is the value of 7 2 f (x) dx. a) Use the graph of f alone to estimate I . b) Use the information in the graphs to tell how many subdivisions N are needed so that the Trapezoid Rule approximation TN will approximate I with error < 10−5 . c) Use the information in the graphs to tell how many subdivisions N are needed so that the Simpson’s Rule approximation SN will approximate I with error < 10−5 . Graph of f ′ Graph of f (3) Graph of f ′′ Graph of f (4) 2) The only information known about a function T and its derivatives is contained in this table: x T (x) T ′ (x) T ′′ (x) 1 2 −2 2 a) Compute 23 T ′ (x) dx. 2 3 6 5 b) Compute 23 T ′′ (x) dx. 3 7 4 −4 3 c) Compute 2 xdx. 4 2 5 7 d) Compute 3 2 xT ′′ (x) dx. Don’t look at b) and c)! Integrate by parts. e) Compute 3 2 x2 T ′′′ (x) dx. And again and again. 3) Calculate four of the following integrals: x cos x2 dx ; x cos2 x2 dx ; x2 cos x dx ; x2 cos2 x dx ; x cos2 x dx . Comment Most people use many parentheses and rewrite the integrands to decrease possible confusion. So x2 cos2 x becomes x2 (cos x)2 and x cos2 x2 becomes x cos2 (x2 ). ...
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## This note was uploaded on 02/29/2012 for the course MATH 152 taught by Professor Sc during the Fall '08 term at Rutgers.

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workshop3 - Workshop 3 1) Suppose f is deﬁned by f (x) =...

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