Mathamatics,

br Show all work ( calculus 11 ) Show that the granted families of twines are orthogonal trajectories of each new(prenominal)wise . Sketch both families of curves on the equal axesx2 y2 r2 , ax by 0 The two comparabilitys are orthogonal trajectories of each other (black circles for x2 y2 r2 , and the red retraces are the family of ax by 0 You give the bounce see that any pair can be go around along the axis with no change of shape2 ) differentiate the departa ) f (x x (1 /2 ) ln x Using the differential 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 gear of product for d (u3 ) hear 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 derivative ySolving for the 2nd derivative y from y4 ) go back an equation of the tangent line to the curve at the given bloom .y ln ln x (e , 0Solving for the cant over of the equation at any point mwe get the derivative use d (lnu (1 /u )du where u lnxm y (x The slope of the tangent line mt ismt mThen we evaluate the value of the slope at x eWe get mt 1 /eUsing the point slope form y m (x-x1 y1 we get the equation of the tangent liney mt (x-x1 y1 where x1 e and y1 0 we get the final resolving powery (1 /e (x - e5 ) Find the first and second derivatives of the functiony cosThe 1st derivativey -sinThe 2nd derivativey -cos6 ) Find 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 surface area decreases at a tread of 1cm^2 /min , play the identify at which the diameter decreases when the diameter is 10cmSince the equation of Surface plain (S ) as a function of diameter (d ) isS d2We get the derivative of both sides with respect 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 meaning decrease8 ) Find the unfavorable numbers of the functions (t 3t4 4t3 - 6t2The critical numbers are found by getting the derivative and equating this to corrects` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the absolute max and absolute min values of f on the given intervalSolution : Get the derivative , equate to zero , solve 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 hundred 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 answer by differentiationSolution by integration . 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 available to make a rap with a material base and an open outperform , find the largest possible volume of the boxSolutionLet x be the width of the square box and y the height 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 point (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 Part 2 of the Fundamental Theorem of conglutination to evaluate the integral , or explain why it does not exista ) The integration of 6 dx surrounded by 5 and -2b ) The integration of (1 3y - y2 ) dy between 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 dictionary . Is it correct ? Other commentsFrom WordwebA straight line or plane that touches a curve or trend surface at a point but 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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