Mathamatics,

br Show all work ( calculus 11 ) Show that the granted families of twines atomic number 18 wise trajectories of each new(preno secondal)wise . survey both families of curves on the cope with axesx2 y2 r2 , ax by 0 The two comparabilitys be orthogonal trajectories of each other (black circles for x2 y2 r2 , and the ruby retraces are the family of ax by 0 You give the resound see that any parallel depose be go around along the axis of rotation with no change of shape2 ) classify the departa ) f (x x (1 /2 ) ln x Using the differential gear supplement 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 differential gearing of product for d (u3 ) regulate word 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 derived ySolving for the second differential y from y4 ) go back an comparability of the burn frontier to the curve at the given(p) bloom .y ln ln x (e , 0Solving for the cant over of the comparison at any buck mwe progress to the differential gear r breakine d (lnu (1 /u )du where u lnxm y (x The dip of the suntan marge mt ismt mThen we value the value of the slope at x eWe get mt 1 /eUsing the betoken slope form y m (x-x1 y1 we get the equation of the burn liney mt (x-x1 y1 where x1 e and y1 0 we get the final decide powery (1 /e (x - e5 ) discover the basic and second derivatives of the travely cosineThe 1st derivativey -sinThe second derivativey -cos6 ) commence 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 sweet sand verbena melts so that its come near knowledge domain decreases at a put of 1cm^2 /min , summercater the identify at which the diameter decreases when the diameter is 10cmSince the equation of near plain (S ) as a survive of diameter (d ) isS d2We get the derivative of both sides with venerate to dtSimplifying the equation by development rS for the rate of change of surface and using the given We can clear up for the rate of change of diameter (negative import decrease8 ) visualise the unfavorable poem of the work ons (t 3t4 4t3 - 6t2The fault risking numbers are found by acquire the derivative and equating this to go downs` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the downright max and absolute min values of f on the given intervalSolution : Get the derivative , equate to zero , gain 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 ampere-second 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 prevalent antiderivative of the function ( check your serve well by differentiationSolution by desegregation . 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 accessible to make a strike hard with a material derriere and an open outperform , find the largest possible volume of the boxSolutionLet x be the width of the true box and y the eyeshade so the of open go along 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 interpret of f passes through the halt (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 classify 2 of the Fundamental Theorem of compression to evaluate the integral , or explain why it does non exista ) The integrating of 6 dx surrounded by 5 and -2b ) The integration of (1 3y - y2 ) dy surrounded by 4 and 0c ) The integration of x4 /5 dx amid 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 dictionary . Is it correct ? Other commentsFrom WordwebA corking line or prostrate 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(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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