# Calculus 1321 Final Practice Exam - MATH 1321 Calculus I...

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MATH 1321 – Calculus ISections 10 and 14Fall 2004Final Exam – Preparation1. Find the following limits:(a)limx2-x2-x-2|x-2|(b)limx7x+ 2-3x-72. Use the Squeeze Theorem to find limx0ex2sin(1/x).3. Find the following limits:(a)limx→∞1-x-3x22x2-7(b) limx→∞9x6-xx3+ 1(c) limx→∞(x2+x-x)4. Which of the following functionsfhas a removable discontinuity ata? If the discon-tinuity is removable find an everywhere continuous functionFsuch thatf(x) =F(x)for allx=a.(a)f(x) =x2-2x-8x+ 2,a=-2(b)f(x) =x-7|x-7|,a= 7(c)f(x) =x3+ 64x+ 4,a=-45. Find the vertical and horizontal asymptotes of the curvey=x2-92x-6,x >3.6. Use the definition of the derivative to findf(x) iff(x) =1 +x.7. Use the definition of the derivative to findf(x) iff(x) =xx+ 1.8. Letf(x) = sin 2x. Use the definition of the derivative to findf(0).9. Letf(x) =x2ifx2mx+bifx >2(a) Find the values ofmandbthat makefcontinuous everywhere.(b) Find the values ofmandbthat makefdifferentiable everywhere.10. Use the definition of differentiability to show thatf(x) =|x-6|is not differentiableata= 6.11. Iff(x) =exg(x), whereg(0) = 2 andg(0) = 5, findf(0).12. Letf(x) =h(x)x,x= 0. Ifh(2) = 4 andh(2) =-3, findf(2).
13. Letf(x) =g(h(x)). Ifh(3) = 6,h(3) = 4,g(3) = 2 andg(6) = 7, findf(3).14. Find the derivativey:(a)y=12πe-x2/2(b)y=sin(3x)x(c)y= (tanx)(2sinx)15. Ify= ln(x2+y2), findy.16. Find equations of the tangent lines to the curvey=x/(x+ 1) that are parallel to thelinex-2y= 2.17. Find an equation of the tangent line to the curvey=exthat passes through the origin.18. Find the point on the parabolay=x2at which the slope of the tangent line is equalto the slope of the secant line betweenA(a, a2) andB(b, b2).19. Find the slope of the tangent line to the curvex3y2-2y=ey-1 at the point (1,0).20. Letf(x) =x2/3.(a) Use the definition of the derivative to show thatf(0) does not exist.(b) Findf(x) forx= 0. (Here you don’t have to use the definition of the derivative.You are allowed to use the power rule.)(c) Show that the graph offhas a vertical tangent line at (0,0).(d) Illustrate part (c) be sketching the graph off.

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Term
Fall
Professor
Mathis
Tags
lim, Mathematical analysis