m251finalprac.pdf - Calculus Practice Final 1. Let F (t ) =...

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Calculus Practice Final1. LetF(t)=t(lnt)-t.(a) FindF0(t).(b) FindZ16lnt dttwo ways: (i.) numerically with the left sum and 4 sub intervals and (ii.) usingthe Fundamental Theorem of Calculus.102. Determine the exact area of the region enclosed byy=x2andy=px.3. Evaluate the following:(a)Z82px dx(b)Z3-11-x2dx(c)Z3-3p9-x2dx(d)Zπ/20ex+sinx dx4. Find the derivative of the following:(a)f(x)=Zxosin(et)dt(b)f(x)=Zx-5et2dt(c)f(x)=Zx2-1et2dt(d)f(x)=Zcosxπ3pt dt(e)f(x)=Z1x4lnt dt(f)f(x)=Zcosxsinxt2dt5. Use Newton’s method to estimate the point of intersection ofy=e-x2andy=xaccurate up to 5decimal places. List allxi’s.6. Evaluate the following limits:(a)limx0+xlnx(b)limx0+1-expx(c)limx4x-4px-2(d)limx1x3+x-2x2-3x+2(e)limx→∞x2ex(f)limx→-∞1000x-27. Determine all exact valuescthat satisfy the conclusions of the Mean Value Theorem for the functionf(x)=x3-2x2+x+2on the closed interval[-1,2].8. A pyramid has heighthand a square base with sidex

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