2. You measure a cubic container and find it to be about 10 cm on each side. From this, you conclude that it holds 1000 cc. However, your measurement is accurate only to within 10.1 cm. (So you can be sure that the side is between 9.9 and 10.1 cm.) A. What are x, f(x), and a in this problem? X = 10 f ( x ) = 1000 a = 10.1 or 9.9 B. Use the tangent line approximation to estimate the error in your value of 1000 for the volume. A ( 10 ) + f' ( 10 ) soiluloa musiq ofa ledal oe) /* wov ed liny jordi - able svn ard enhussam envoy maldong eiri ni ad il'voy towel Bleit ard 10 891G SHT . b nendo ant COP Jon x dulw C. Give the percent error in your measurement of the length of the side. (X)1 = Wel nodonut some sriT .sued endsmixonqqs of lupe vitamixdiggs al A giffenouslessnil s svip lliw nouismixonqqs soil insensi nT D. Give the percent error in your estimate of the volume. Lov vilann aroy Janw Winabi of jedmeman ,wollot ash empidony add to itsso n mud ov e'si won 3. If a right triangle has legs 6 and 8, its hypotenuse is 10. The triangle will be inscribed within a circle with area 25xt . (The hypotenuse will be the diameter of the circle.) A. Suppose one leg of the triangle is known to be exactly 6, but the other leg is known to be 8 with an error of th. What are x, f(x), and a in this problem? f ( x ) + f '( x ) ( a - x )B. Use a tangent line approximation to estimate the area of the circumscribed circle. C. Now consider the sphere that just contains the triangle (so the hypotenuse is the diameter of the sphere). Use a tangent line approximation to estimate the volume of this sphere. jarl ( )g noworigi emoa al snarlT : meldong philwollon ers boy esvin basit TOY seoqque bashingY is blue allnu to madmen eni to noidoni/ s es (ellob ni) c dionq edrisesiqs x lla tol Se (x /q sd) won asob Jud ,Ibilqxe zi (x)q notionul sift delw won> J'nesob Howona es broil woy ,wol Isdavie = (cos)q 1shi aworl cals bneil woY bright way jud ,mutomboriggs anil ansprint phiau (EDS)q sJEmixonqqs of noltemoti .ed illw golfsmixgiggs jard edsloos wod won of anew vil697 4. Suppose the point , is on the curve sinx , siny =C, where C is a constant. Use x (coy the tangent line approximation to find the y-coordinate of the point on the curve with x- in92 coordinate ~ + . Be sure to show all your work. 5. Use tangent line approximation to derive an estimate for (1+x)", when x is near 0, and n is any real number. F ( x ) + + " ( x ) ( a- x )aA Page 4 of 4 AP Calculus AB Practice: Tangent Line Approximation xonggA aniJ iaphsT :9013519 User Name: Date: (print clearly) Instructor: 6. Use tangent line approximation to estimate $2390 (to seven decimal places), recognizing that 74 = 2401. Show all your work. ( ( x ) = x 4 3 f ( x ) = 1 4 x 6=2 40 1 + Portal sworedogvn wild ca) alprish off enisingo deut ford merge ard joblenos woll . Suppose your friend gives you the following problem: There is some function p(x) that represents profit p (in dollars) as a function of the number of units sold x. Your friend doesn't know what the function p(x) is explicitly, but does know that p'(x) = 2 for all x. Your friend also knows that p(200) = 3175.24. Now, your friend has enough information to approximate p(203) using tangent line approximation, but your friend really wants to know how accurate that approximation will be. The question to you then is: What can you tell your friend about the accuracy of the tangent line approximation for p(203), given the above information about the function p? (You may explain yourself mathematically, or by presenting graphs, or just by discussing in complete sentences.) w wov lis worle of squa o P Ca ) = P ( 200 ) +p' ( 200 ) ( 203 - 200 ) = 3/75. 24 + 2 ( 3) 3181. 24 box redmup Isa You at n