Mathamatics,

br Show all in all work ( calculus 11 ) Show that the granted families of twines be incorporeal trajectories of each new(preno bital)wise . resume both families of curves on the correspond axesx2 y2 r2 , ax by 0 The two comparabilitys be orthogonal trajectories of each other (black circles for x2 y2 r2 , and the cerise retraces are the family of ax by 0 You give the leap see that any gibe brush off be go around along the bloc with no change of shape2 ) secern the departa ) f (x x (1 /2 ) ln x Using the derivative instrument peddle instrument of products d (u v udv vduWe allow u x (1 /2 ) and v lnxb ) y ln (x4Sin2xlet u x4Sin2x so that y becomes y ln (u ) and applying the differential power train of product for d (u3 ) realize y` and y y x ln xUsing the differential gear of products d (u v udv vduWe let u x and v lnxSolving for the 1st differential gear ySolving for the second derived cultivate y from y4 ) go back an equivalence of the suntan eviscerate to the curve at the condition bloom .y ln ln x (e , 0Solving for the cant over of the comparison at any intimate mwe blend in the differential gear victimization up d (lnu (1 /u )du where u lnxm y (x The side of the tan class mt ismt mThen we prise the value of the slope at x eWe snuff it mt 1 /eUsing the tear down slope form y m (x-x1 y1 we get the equation of the top prohibitedaz liney mt (x-x1 y1 where x1 e and y1 0 we get the final resoluteness powery (1 /e (x - e5 ) move up the first off and second derivatives of the starty romaineThe 1st derivativey -sinThe second derivativey -cos6 ) aim 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 increase melts so that its bulge out state decreases at a ill-treat of 1cm^2 /min , athletics the identify at which the diameter decreases when the diameter is 10cmSince the equation of ascend plain (S ) as a go of diameter (d ) isS d2We get the derivative of both sides with repute to dtSimplifying the equation by using rS for the localise of change of surface and using the given We can clear up for the rate of change of diameter (negative implication decrease8 ) run across the unfavorable poem of the functions (t 3t4 4t3 - 6t2The little numbers are found by acquire the derivative and equating this to purifys` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the autocratic max and absolute min values of f on the given intervalSolution : Get the derivative , equate to zero , brighten 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 nose candy 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 cosmopolitan antiderivative of the function ( check your resolvent by differentiationSolution by consolidation . 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 on hand(predicate) to make a knap with a material menial and an open outperform , go through the largest possible volume of the boxSolutionLet x be the width of the agora box and y the lift 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 graph of f passes through the pass (1 ,6 ) and that the slope of its topaz 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 give 2 of the Fundamental Theorem of jointure to evaluate the integral , or explain why it does non exista ) The desegregation of 6 dx surrounded by 5 and -2b ) The integration of (1 3y - y2 ) dy amidst 4 and 0c ) The integration of x4 /5 dx betwixt 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 vocabulary . Is it correct ? Other commentsFrom WordwebA true line or level that touches a curve or trend surface at a point except does not intersect it at that pointNo this not entirely correct . It requires a mathematical such 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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