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Let f be the function defined on x by f x

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513. Letfbe the function defined on-∞< x <byf(x) =integraldisplayx0t(et-1)dtAt how many pointsacanf(a) be a local minimum (relative minimum)?(a)0(b)1(c)2(d)3(e)4
14. A line segmentLpassing through the point (1,1) has its endpoints lying on thex-axis andy-axisas shown in the figure. What is the shortest possible length of such a line segment?
15. If Newton’s method is applied to find the critical point of thef(x) = sinx-lnx, i.e., a point wheref(x) = 0, which of the following iteration formulas should be obtained?
616. Find the value of the integralintegraldisplayπ406 tan2xsec2x dx.
17. Find the value of the definite integralintegraldisplayln203ex(1 +ex)2dx.(a)12(b)23(c)1(d)2(e)3
18. Find the limitlimn+1nnsummationdisplayk=1cos6n.
719. Given the graph of the functiony=f(x) as shown below, findintegraldisplay50|f(x)|(f(x))2dx.36-3xyy=f(x)

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Term
Fall
Professor
TK Lam

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