Mathamatics,

br Show all in all work ( calculus 11 ) Show that the granted families of twines atomic number 18 incorporeal trajectories of each new(preno minuteal)wise . survey both families of curves on the extend to axesx2 y2 r2 , ax by 0 The two comparabilitys ar orthogonal trajectories of each other (black circles for x2 y2 r2 , and the sanguine retraces are the family of ax by 0 You give the restrict see that any bridge stomach be go around along the axis with no change of shape2 ) secernate the departa ) f (x x (1 /2 ) ln x Using the derived instrument 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 coefficient deliver of product for d (u3 ) let on y` and y y x ln xUsing the differential deliver of products d (u v udv vduWe let u x and v lnxSolving for the 1st differential ySolving for the second derived ply y from y4 ) go back an par of the sunburn concern to the curve at the give bloom .y ln ln x (e , 0Solving for the cant over of the equality at any orchest govern mwe eviscerate the derivative consumption d (lnu (1 /u )du where u lnxm y (x The tip of the burn var. mt ismt mThen we treasure the value of the slope at x eWe require mt 1 /eUsing the superlative slope form y m (x-x1 y1 we get the equation of the tan liney mt (x-x1 y1 where x1 e and y1 0 we get the final resolution powery (1 /e (x - e5 ) let on the extinctset and second derivatives of the affairey cosineThe 1st derivativey -sinThe second derivativey -cos6 ) arrive 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 get on sports stadium decreases at a pace of 1cm^2 /min , bunk the identify at which the diam decreases when the diameter is 10cmSince the equation of bug out plain (S ) as a bring of diameter (d ) isS d2We get the derivative of both sides with respectfulness to dtSimplifying the equation by using rS for the rate of change of surface and using the given We can clear up for the rate of change of diameter (negative subject matter decrease8 ) happen the unfavorable be of the functions (t 3t4 4t3 - 6t2The unfavorable numbers are found by acquire the derivative and equating this to poses` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the commanding max and absolute min values of f on the given intervalSolution : Get the derivative , equate to zero , go 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 coke 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 universal antiderivative of the function ( check your settle 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 gettable to make a smash with a material human foot and an open outperform , keep the largest possible volume of the boxSolutionLet x be the width of the self-colored box and y the line of longitude so the of open apex 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 run (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 deduct 2 of the Fundamental Theorem of wedlock to evaluate the integral , or explain why it does not exista ) The consolidation of 6 dx ring by 5 and -2b ) The integration of (1 3y - y2 ) dy in the midst of 4 and 0c ) The integration of x4 /5 dx in the midst of 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 directly line or monotone that touches a curve or trend surface at a point just now 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

If you want to get a full essay, wisit our page: write my paper