Mathamatics,

br Show only work ( calculus 11 ) Show that the granted families of twines be irrelevant trajectories of each new(prenomoal)wise . field of study both families of curves on the satisfactory axesx2 y2 r2 , ax by 0 The two comparabilitys argon orthogonal trajectories of each other (black circles for x2 y2 r2 , and the rubor retraces are the family of ax by 0 You give the leaping see that any gibe quarter be go around along the bloc with no change of shape2 ) differentiate the departa ) f (x x (1 /2 ) ln x Using the derived live instrument of products d (u v udv vduWe let u x (1 /2 ) and v lnxb ) y ln (x4Sin2xlet u x4Sin2x so that y becomes y ln (u ) and applying the derivative instrument set up of product for d (u3 ) disclose y` and y y x ln xUsing the differential monger of products d (u v udv vduWe let u x and v lnxSolving for the 1st differential instrument ySolving for the second derived y from y4 ) go back an par of the suntan path to the curve at the precondition bloom .y ln ln x (e , 0Solving for the cant over of the equation at any period mwe mature the derivative accustom d (lnu (1 /u )du where u lnxm y (x The sky of the burn grade mt ismt mThen we survey the value of the slope at x eWe breed mt 1 /eUsing the flower slope form y m (x-x1 y1 we get the equation of the tipaz liney mt (x-x1 y1 where x1 e and y1 0 we get the final result powery (1 /e (x - e5 ) cause the surfaceset and second derivatives of the purposey cosineThe 1st derivativey -sinThe second derivativey -cos6 ) predominate y `y (2x 3 )1 /2Applying dun n un-1 where u 2x 3y (1 /2 (2x 3 )-1 /2 (2y (-1 /2 (2x 3 )-3 /2 (2y - (-3 /2 (2x 3 )-5 /2 (2y 3 (2x 3 )-5 /27 ) If a snowball melts so that its pay back theatre of operations decreases at a trample of 1cm^2 /min , pushover the identify at which the diameter decreases when the diameter is 10cmSince the equation of coat plain (S ) as a break of diameter (d ) isS d2We get the derivative of both sides with deference to dtSimplifying the equation by victimization rS for the respect of change of surface and using the given We can clear up for the rate of change of diameter (negative marrow decrease8 ) see to it the unfavorable number of the functions (t 3t4 4t3 - 6t2The little numbers are found by getting the derivative and equating this to sics` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the direct max and absolute min values of f on the given intervalSolution : Get the derivative , equate to zero , decide for x , then get f (x )a ) f (x 3x2 - 12x 5 (0 ,3 0 6x -12x 2f (2 3 4 - 12 2 5 -7b ) f (x 2x3 - 3x2 - 12x 1 ( -2 , 30 6 x2 - 6x - long degree Celsius x2 -x - 20 (x-2 (x 1x1 2x2 -1f (x1 2 8-3 4-12 2 1f (x1 16 -12 3 1f (x1 -19f (x2 2 (-1 )-3 (1 12 1f (x2 -2-3 12 1 8 c ) f (x ( x2 - 1 )3 (-1 , 20 3 (x2-1 )2 (2x0 6x (x2-1 )2x1 0x2 1x3 -1f (x1 1f (x2 0f (x3 0d ) f (x x (x2 1 ( 0 , 2f (x x (x2 1 )-10 - x (x2 1 )-2 (2x (x2 1 )-10 -2x2 (x2 1 )-2 (x2 1 )-10 -2x2 (x2 1 )-1 10 -2x2 (x2 10 -x2 1x (-1 )1 /2 imaginaryf (x imaginaryd ) f (x ( ln x /x (1 ,30 - (lnx )x-2 x-1 x-10 1 - ln xx ef (x 1 /e10 ) Find the most general antiderivative of the function ( check your dissolving agent by differentiationSolution by integrating . C de nones a constanta ) f (x 10 /x9f (x 10 x-9F (x (-10 /8 )x-8 C b ) f (x 6 (x )1 /2 - (x )1 /6F (x 6 (2 /3 )x3 /2 - (6 /7 )x7 /6 C11 ) If 1200 cm2 of material is forthcoming to make a pick apart with a material stall and an open outperform , find the largest possible volume of the boxSolutionLet x be the width of the substantial box and y the bloom so the of open top considering 5 sides1200 x2 4xyy (x2-1200 /4xy - (x2-1200 (4x )-2 (4x )-1 (2xy - (x2-1200 8x2y 7 x2 12000 7 x2 1200x 1200 /7x 171 .43 cmy 41 .11 cmlargest volumen vv x x yv 1208150 .

75 cm312 ) Write the composite function in the form f (g (x Identify the inner function u g (x ) and the out function y f (u Then find the derivative dy /dxy (4 3x )1 /2let u 4 3xy u1 /2dy (1 /2 u-1 /2dudy (1 /2 (4 3x ) -1 /2 (3dxdy /dx (3 /2 (4 3x ) -1 /213 ) Find the derivative of the functiona ) f (t (1 tan t )1 /3SolutionDtf (t (1 /3 (1 tan t )-2 /3 (sec2t b ) y tan2 (3Solutiondy /d 2tan (3 (3dy /d 6tan (314 ) Find the most general antiderivative of the function ( check your answer by differentiationa ) f (x x20 4x10 8SolutionAxf (x (1 /21 ) x21 (4 /11 )x11 8x Cb ) f (x 2x 3x1 .7SolutionAxf (x (2 /2 )x2 (3 /2 .7 )x2 .7 CAxf (x x2 (3 /2 .7 )x2 .7 Cc ) f (x (x3 )1 /4 (x4 )1 /3Solutionf (x x3 /4 x4 /3Axf (x (4 /7 ) x7 /4 (3 /7 )x7 /3 Cd ) f (u u^4 3 (u )^1 /2 /u^215 ) Find ff ` (x 2 - 12x , f (0 9 , f (2 15Solution1st Antiderivative of f (xf (x 2x - (12 /2 )x2 Cf (x 2x - x2 C2nd Antiderivativef (x (2 /2 ) x2 - (1 /3 ) x3 Cx C2f (x x2 - (1 /3 ) x3 Cx C23rd Antiderivativef (x (1 /3 )x3 - (1 /12 ) x4 (C /2 )x2 C2x C3 let (C /2 C1f (x (1 /3 )x3 - (1 /12 ) x4 C1x2 C2x C3f (0 9 C3f (2 (1 /3 )23 - (1 /12 ) 24 C1 22 C2 2 9 1515 (8 /3 ) - (16 /12 4 C1 2 C2No Solution : requires additional given f (x ) to solve16 ) Given that the graphical record of f passes through the capitulum (1 ,6 ) and that the slope of its tangent line at ( x , f (x ) is 2x 1 , find f (2SolutionThe slope is the 1st derivativef (x 2x 11st Antiderivativef (x x2 x CUsing the intersection to solve for C6 f (1 1 1 CC 4We get the final equation f (xf (x x2 x 4So thatf (2 4 2 4f (2 1017 ) Find the differential of the functiona ) y cos (xdy -sin (x (dxdy - (sin (x )dxb ) y x ln xc ) y (1 t2 )1 /2dy (1 /2 (1 t2 )-1 /2 (2tdtdy t (1 t2 )-1 /2 dt18 ) Use fail 2 of the Fundamental Theorem of sexual union to evaluate the integral , or explain why it does not exista ) The integrating of 6 dx skirt by 5 and -2b ) The integration of (1 3y - y2 ) dy amid 4 and 0c ) The integration of x4 /5 dx amidst 1 and 0d ) The integration of (3 / t4 )dt between 2 and 1e ) The integration of cos )d ( between 2 ( and19 ) Find a definition of `tangent` in a lexicon . Is it correct ? Other commentsFrom WordwebA cracking line or rag that touches a curve or trend surface at a point entirely does not intersect it at that pointNo this not entirely correct . It requires a mathematical such(prenominal) as a line with the same slope as the curve at the point of intersectionxy ...If you take to get a full essay, order it on our website: Ordercustompaper.com

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