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# Ch 4 - Cth £1 ~I “'J‘csrzwim mm 5 www i_Am_t"...

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Unformatted text preview: Cth £1 ~I “'J‘csrzwim mm 5 www- i! ._Am_t" Ju;uq+[ue& (IAJej {wife I'm—hosra/S) T; Lu. HA r 277 Eyakrglg, C, Z, 1'3 D‘Sina-«Q E345“ 133:3: Li: 3 :N+¢I)r=~ ‘How (9 1 §+R+wﬁoh ii £S+£h~m¢ﬁ~3 Wifk Sum—.5 Ll. s [Zi-LMAK Sums ad nghdtt I~+tjrqr\$ . AWL“ \ZKIM 5“ mm gm; ,0. 310 3D wadv~u~s?“‘lﬂ 4) AW) Swwx. FOFMAW(°LS l ,é 'Mww :6.“ch «9 my»? . («ls Lflg Pmpuﬁﬂ dj 0433Mme ZEN—th / #1 VCO) -} 1. Consider f(x) = 2 — x2 on the interval [0,3] a) Sketch the graph of the curve y = f(x). b) What is the average value of f(x) on [0,3]? 0) At what value or values of x in [0,3] is the average value of f(x) attained? 2. Evaluate the following a) ff ——1——————~an xVI+\/; 3. Evaluate the integrals by graphical observation a) f32xdx+f:1\/l—x2 (ix b) The natural logarithm function is defined as ln(x) = 1x;— alt . Suppose we want to estimate the value of secytany 2+secy c)f dy 1n<x> If:- 0) Write out the linearization of ln(x) near x = 1. d1 t by numerical integration via the trapezoidal rule for n = 3. 4. a) Estimate the minimum number of subintervals needed to approximate the integral with an error magni— ' tude less than 10'4 by the trapezoidal rule f_11(x2 +1)de _ b) Use the Max—Min Inequality to find upper and lower bounds for the value of this definite integral ...
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Ch 4 - Cth £1 ~I “'J‘csrzwim mm 5 www i_Am_t"...

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