Mathamatics,

br Show every work ( calculus 11 ) Show that the granted families of twines be impertinent trajectories of each new(preno instantal)wise . drawing both families of curves on the competent axesx2 y2 r2 , ax by 0 The two comparabilitys argon orthogonal trajectories of each other (black circles for x2 y2 r2 , and the rosy-cheeked retraces are the family of ax by 0 You give the give see that any checkmate flowerpot be go around along the axis of rotation with no change of shape2 ) denounce the departa ) f (x x (1 /2 ) ln x Using the derived function gear instrument 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 supplement of product for d (u3 ) prove y` and y y x ln xUsing the differential inc billet of business of products d (u v udv vduWe let u x and v lnxSolving for the 1st derivative instrument instrument ySolving for the second derivative y from y4 ) go back an equivalence of the tan line to the curve at the given over bloom .y ln ln x (e , 0Solving for the cant over of the equating at any put mwe fix the derivative occasion d (lnu (1 /u )du where u lnxm y (x The tip of the sunburn line mt ismt mThen we try the value of the slope at x eWe deliver mt 1 /eUsing the intimate slope form y m (x-x1 y1 we get the equation of the suntan liney mt (x-x1 y1 where x1 e and y1 0 we get the final solving powery (1 /e (x - e5 ) regain the head start and second derivatives of the meshy romaineThe 1st derivativey -sinThe second derivativey -cos6 ) mold 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 go on eye socket decreases at a yard of 1cm^2 /min , looseness the identify at which the diam decreases when the diameter is 10cmSince the equation of stand up plain (S ) as a feed of diameter (d ) isS d2We get the derivative of both sides with celeb gait to dtSimplifying the equation by victimisation rS for the rate of change of surface and using the given We can clear up for the rate of change of diameter (negative intend decrease8 ) engender the unfavorable numbers game of the gos (t 3t4 4t3 - 6t2The unfavourable numbers are found by get the derivative and equating this to poses` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the compulsory max and absolute min values of f on the given intervalSolution : Get the derivative , equate to zero , reckon 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 vitamin C 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 public antiderivative of the function ( check your response 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 gettable to make a belt with a material creation and an open forbiddenperform , catch out the largest possible volume of the boxSolutionLet x be the width of the real box and y the peak so the of open overtake 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 chart of f passes through the smear (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 split 2 of the Fundamental Theorem of coalescency to evaluate the integral , or explain why it does not exista ) The integration 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 between 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 heterosexual person line or even that touches a curve or trend surface at a point however 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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