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# HON MATH 1551

LSU

GPA 3.72

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This 6 page Class Notes was uploaded by Madison Gottlieb Sr. on Tuesday October 13, 2015. The Class Notes belongs to MATH 1551 at Louisiana State University taught by H. Kuo in Fall. Since its upload, it has received 24 views. For similar materials see /class/222633/math-1551-louisiana-state-university in Mathematics (M) at Louisiana State University.

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Date Created: 10/13/15

1 to Math 15512 Review Exercises Fall 2006 i i i 1 1 Evaluate the limit lim 7 7 7 x7gt0 x x1 x ax 7 if x lt 2 Suppose a function x is de ned by x 5 if x 2 x2 bx if x gt 2 03 F U a T 00 Find the values of a and b so that x is continuous at x 2 3 1 Find the vertical asymptotes of the curve y 3 x 7 4x Evaluate the limit 131 ltx2 3x 7 Find the horizontal asymptotes of the curve y 1 Use the de nition of derivative to nd f a for the function x x2 7 3x Here a is any xed real number Find the x coordinates of the points on the curve y x3 7 x2 7 x 1 where the tangent is horizontal 1 7 Evaluate the limit lim x70 x2 Let x2 3xem Find fO ii at the point 2 3 Find an equation of the tangent line to the curve y Let x sin4x 7 cos4x Find f x d Let y izz 7 3x Find Ty Z1 x439 d Use the implicit differentiation to nd Ty for the curve x2 y2 xy 1 1 1 Let x tanx Find g x Z 0 i Check whether the function f x3 x lt 0 7 2 Let f be a function de ned by x m is differentiable at 0 and if so nd f 0 Let x tan 12x sin 1x Find f x 2 Evaluate the limit lim Hoe n Solve the equation coshx 7 sinhx 3 Let y 352 Find 21 xe 2 Find the arc length of the curve y 7132 1g x g 4 OJ OJ OJ q OJ 0 OJ a DJ 1 OJ to 4 Find the absolute maximum and minimum of the function x x 7 Evaluate the integral le 1 Evaluate the integral x4 71 Let y log2 l7 7 3x Find dy Two cars start moving from the same point One travels north at 30 mih and the other travels east at 40 mih At what rate is the distance between the cars increasing 30 minutes later Find the critical numbers of the function x x13x 1 Find the intervals on which the function x xze m is decreasing Use the second derivative test to nd the local maximum and minimum values of the function x x 7 2sinx7 0 g x g 7139 Evaluate the limit lim x ln x x704r Suppose the derivative f x of a function x is given by f x x 3e m Check that there is exactly one in ection point in the graph of y x and nd its x coordinate 7L Express the limit lim 2 7 5xAx as a de nite integral on the interval 07 2 Hoe Let 35 1t2dt Find f 1 Find the antiderivative of x 3 7 21 xz 1 satisfying F1 3 Let gx 0 1112 Evaluate the integral 521 dx 0 tanx 1 Walt 0 g x 7r2 Find gx 7r4 Evaluate the integral sec xtan x dx 0 2dx Evaluate the integral x2x3 25 dx 8 Evaluate the integral mi dx 1 1 Find the area of the region bounded by y em y cos x7 and x 7r2 x5 gtd 7 x V17 x2 Revolve the region bounded by y x27 y 07 x 1 about the x axis Find the volume of the resulting solid Use the method of disks to nd the volume of a sphere of radius r 4 to 43 4 q 4 U 4 a 4 4 00 4 to U Q U H U to U l U 00 U to Evaluate the limit limolt x7 1 Let R be the region bounded by y em y 17 and x 2 Revolve R about the line x 3 Use the method of cylindrical shells to set up an integral but do not evaluate for the volume of the resulting solid An aquarium 20 ft long7 10 ft Wide7 and 12 ft deep is half full of water Find the work required to empty the aquarium by pumping all of the water to the top of the aquarium Note the water density is 625 lbft3 Find the arc length of the curve y cosh x7 0 g x g 3 1 1 gt x x1 x 39 Evaluate the limit lim 5 7 x77 x 2 if x lt 37 Suppose a function x is de ned by x at7 if x 37 x2 bx7 if x gt 3 Find the values of a and b so that x is continuous on 7007 00 3 7 1 Find the vertical asymptotes of the curve y x 7 4x Evaluate the limit 13ng ltx2 x 7 x2 i i i 1 7 M Find the horizontal asymptotes of the curve 1 2x 1 7 Evaluate the limit lim x700 Use the de nition of derivative to nd f a for the function x 3 Here a is a xed positive number Find the x coordinates of the points on the curve x x3 7 3x2 25 where the tangent line has a slope 6 Let x Find H2 7 x 71x239 Let x3 1 2x 32 Find fO The position function of a particle is given by s t3 t2 7 5257 t 2 0 When does the particle reach a velocity of 3msec Find an equation of the tangent line to the curve y 3 2x2 4 at the point 2 0 sin El tthl tl vauae eimi 91m20tan0 70 Find all points on the graph of the function x sin2x 3cosx at which the tangent line is horizontal i i i i i i d Use the implicit differentiation to nd Ty for the curve 21 y2 xy 1 Let x sin 12x71tan 1x2 Find we 3 a 00 a to 70 7 H 7 7 OJ 7 q 7 U 7 a 7 1 7 00 7 to 8 O 8 H 8 to 8 OJ to 8 Evaluate the integral 1 Let x secx Find f i i i i 2 3n Find the limit lim 1 7 Hoe n Let y 3m 7 2x Find the y di erential A kite 75 ft above the ground moves horizontally at a speed of 8 ftsec At what rate is the angle between the string and the horizontal decreasing when 150 ft of string have been let out Find the critical numbers of the function x sinhx coshx 7 6x Find the critical numbers of the function x x23x 4 16 Find the absolute maximum and minimum values of x x2 7 1 g x g 4 1 Use the rst derivative test to nd local maximum and minimum values of the function x3 3x2 7 9x Use the second derivative test to nd local maximum and minimum values of the function x x 7 sinx7 0 g x g 7139 Suppose f x x1x712x7 3e4m Find the intervals on which 1 is increasing Suppose f x 2 7 ln 7 1 Find the intervals on which 1 is concave upward 1 Find points of in ection on the curve x xe A piece of wire 1 m long is cut into two pieces One piece is bent into a square and the other is bent into a circle How should the wire be cut so that the total area enclosed is a minimum Let x m11t2dt Find fl 1 Evaluate the integral 7 dx 0 1112 Evaluate the integral 5 dx 0 Evaluate the integral cot2 xdx 1 V 2 7 x2 ln x2 1 Evaluate the integral dx Find the area of the region bounded by y em and y sinx for 0 g x g 7139 m7 2 Evaluate the integral 7 dm 72 V1 1 x4 Let R be the region bounded by y em y 17 and x 2 Revolve R about the line x 75 Use the method of cylindrical shells to set up an integral but do not evaluate for the volume of the resulting solid 8 q 8 U 8 a 8 1 8 00 8 to 100 101 102 103 Find the average value of the function x Lt 2PF ey x 1nd 1 3 20 xlt3 x Find the arc length of the curve y gxsZ 0 g x g 3 Find the arc length of the curve y ln sec x7 0 g x 7r4 Evaluate the limit lim t74 2 7 1 1 6m 1 Find the horizontal asymptotes of the curve y 5 7 Evaluate the limit lt x2 x 7 Determine whether or not f 0 exists for the function 2 1 Mg 7 z q x0 Find the x coordinates of the points on the curve y x3 7 x2 7 2x 5 where the tangent is horizontal Let y x2 x Suppose 2 71 and f 2 3 Find 7y 2 13 x Find an equation of the tangent line to y 1 2 at the point where x 1 13 i i i 0 i 1 7 cos0 Evaluate the limit a shin m b 13 Differentiate the function7 but do not simplify wwm7Wmm HMW b 1 81114952 Find the slope of the tangent line to the curve x3 y3 3xy at the point g dig Let y Find dmg x139 Lag xlnpx77xFmde71 g Find the critical numbers of the function x 7 12x 1 3 The altitude of a triangle is increasing at a rate of 2 cmsec While the area of the triangle is decreasing at a rate of 5 cmZsec At what rate is the base of the triangle changing when the altitude is 3 cm and the area is 15 cm2 Find the absolute maximum and absolute minimum values of the function Let x x 7 sin x7 0 g x g 7139 Find the intervals on which the fufnction f is increasing 104 105 106 107 108 109 11 111 11 to 11 11 11 11 117 118 11 to 12 121 12 12 0 Evaluate the integrals a 0 03 F U a 0 03 Let x 4 7 2mg Find the intervals on which the graph of f is concave upward If sinhz 5 Find coshz Evaluate the limit mliHnoiJz2 5ze m Find the area of the largest rectangle that can be inscribed in the ellipse 2 9342 1 Given that the graph of 1 passes through the point 07 5 and that the slope of its tangent line at z is cosz 1 sin m nd f7r2 Let fa12m1tt2dt Find f 1 3 Evaluate the integral 9 7 2 dm 73 cm ifmZO 7 2 F d d 1 ifzlt0 m AW Let x 12 1 75 1 in b 72 W 0 2z 2 Evaluate the integral 2 1 z z4 2 1 dm 72 dx 1 2 Evaluate the integrals a m 7 7 dm b sec zsec z 1 tan z dm 1 Evaluate the limit lim 7 lt0 i 13 2 1 43 E 4 00 71 71 71 71 1 Evaluate the integral dm 1 m Find the area of the region enclosed by the curves y 2 and y z 2 The base of a solid is a circular disk with radius r Parallel cross sections perpendicular to the base are squares Find the volume of the solid Rotate the region enclosed by the curves yz z and z 2y about the line z 71 Set up two integrals7 one in z and another in y to nd the volume of this solid of revolution A cable that weighs 2 lbft is used to lift 17 000 lb of coal up a mineshaft 600 ft deep Find the work done 1 1 Find the arc length of the curve y Ems 27 1 g x g 2 1 Verify the formula A 47139 2 for the surface area of a sphere of radius r Rotate y m2 0 g x g 17 about the y axis Find the area of the resulting surface

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