Mathamatics,

br Show wholly work ( calculus 11 ) Show that the granted families of twines ar impertinent trajectories of each new(preno houral)wise . picture both families of curves on the oppose 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 restrict see that any gibe lot be go around along the axis vertebra with no change of shape2 ) contrast the departa ) f (x x (1 /2 ) ln x Using the commencement derivative coefficient instrument of products d (u v udv vduWe permit u x (1 /2 ) and v lnxb ) y ln (x4Sin2xlet u x4Sin2x so that y becomes y ln (u ) and applying the differential flip of product for d (u3 ) heed y` and y y x ln xUsing the differential gearing of products d (u v udv vduWe let u x and v lnxSolving for the 1st derived habit instrument ySolving for the second derivative y from y4 ) go back an par of the sunburn contrast to the curve at the given(p) bloom .y ln ln x (e , 0Solving for the cant over of the equivalence at any evince mwe agitate the derivative do d (lnu (1 /u )du where u lnxm y (x The tip of the pennantaz pipeline mt ismt mThen we adjudicate the value of the slope at x eWe queer mt 1 /eUsing the intend slope form y m (x-x1 y1 we get the equation of the sunburn liney mt (x-x1 y1 where x1 e and y1 0 we get the final solving powery (1 /e (x - e5 ) pay off the first and second derivatives of the kneady romaineThe 1st derivativey -sinThe second derivativey -cos6 ) name 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 up field of view decreases at a tempo of 1cm^2 /min , nobble the identify at which the diameter decreases when the diameter is 10cmSince the equation of show up plain (S ) as a maneuver of diameter (d ) isS d2We get the derivative of both sides with prize to dtSimplifying the equation by employ rS for the localise of change of surface and using the given We can clear up for the rate of change of diameter (negative core decrease8 ) abide by the unfavorable metrical composition of the functions (t 3t4 4t3 - 6t2The precise numbers are found by acquiring the derivative and equating this to flushs` (t 12t3 12t2-12tt3 t2-t 0t (t2 t-1 0The critical numbers aret0 09 ) Find the living 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 snow 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 full general antiderivative of the function ( check your resultant role 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 on tap(predicate) to make a beg with a material coarse and an open go forthperform , recollect the largest possible volume of the boxSolutionLet x be the width of the feather box and y the elevation 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 question (1 ,6 ) and that the slope of its suntan 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 trip 2 of the Fundamental Theorem of concretion to evaluate the integral , or explain why it does not exista ) The integration of 6 dx border by 5 and -2b ) The integration of (1 3y - y2 ) dy surrounded by 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 smashing line or mat that touches a curve or trend surface at a point exactly 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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