11 x1 t12 05 curve sketching (2013)

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<ul><li><p>Curve Sketching </p></li><li><p>Curve Sketching Look for; </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p>Look for; </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p><p> 0concavity in change a is thereand 0 if inflection ofpoint 4</p><p>xf</p><p>xf</p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p><p> 0concavity in change a is thereand 0 if inflection ofpoint 4</p><p>xf</p><p>xf</p><p>is; curveA </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p> 0 if increasing xf</p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p><p> 0concavity in change a is thereand 0 if inflection ofpoint 4</p><p>xf</p><p>xf</p><p>is; curveA </p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p> 0 if increasing xf</p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p><p> 0concavity in change a is thereand 0 if inflection ofpoint 4</p><p>xf</p><p>xf</p><p>is; curveA </p><p> 0 if decreasing xf</p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p> 0 if increasing xf</p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p><p> 0concavity in change a is thereand 0 if inflection ofpoint 4</p><p>xf</p><p>xf</p><p>is; curveA </p><p> 0 if decreasing xf</p><p> 0 if up concave xf</p></li><li><p>Curve Sketching 0,0,</p><p>1 e.g.ity discontinu of points yx</p><p>xy</p><p> xfy curve On the</p><p> 0 occur when points stationary 1 xf</p><p>Look for; </p><p> 0 if increasing xf</p><p>xyxx</p><p>xy ,0,1</p><p> e.g. asymptotes </p><p> 0,0 ifpoint turningmaximum 2 xfxf</p><p> 0,0 ifpoint turningminimum 3 xfxf</p><p> 0concavity in change a is thereand 0 if inflection ofpoint 4</p><p>xf</p><p>xf</p><p>is; curveA </p><p> 0 if decreasing xf</p><p> 0 if up concave xf</p><p> 0 ifdown concave xf</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>63</p><p>3</p><p>dx</p><p>yd</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>0 occur when points Stationary dx</p><p>dy6</p><p>3</p><p>3</p><p>dx</p><p>yd</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>0 occur when points Stationary dx</p><p>dy</p><p>09123 i.e. 2 xx</p><p>63</p><p>3</p><p>dx</p><p>yd</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>0 occur when points Stationary dx</p><p>dy</p><p>09123 i.e. 2 xx</p><p> 031</p><p>0342</p><p>xx</p><p>xx</p><p>63</p><p>3</p><p>dx</p><p>yd</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>0 occur when points Stationary dx</p><p>dy</p><p>09123 i.e. 2 xx</p><p> 031</p><p>0342</p><p>xx</p><p>xx</p><p>3or 1 xx</p><p>63</p><p>3</p><p>dx</p><p>yd</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>0 occur when points Stationary dx</p><p>dy</p><p>09123 i.e. 2 xx</p><p> 031</p><p>0342</p><p>xx</p><p>xx</p><p>3or 1 xx</p><p>63</p><p>3</p><p>dx</p><p>yd</p><p>06 </p><p>1216,1when 2</p><p>2</p><p>dx</p><p>ydx</p></li><li><p>596 curve Sketch the e.g. 23 xxxy</p><p>9123 2 xxdx</p><p>dy</p><p>1262</p><p>2</p><p> xdx</p><p>yd</p><p>0 occur when points Stationary dx</p><p>dy</p><p>09123 i.e. 2 xx</p><p> 031</p><p>0342</p><p>xx</p><p>xx</p><p>3or 1 xx</p><p>63</p><p>3</p><p>dx</p><p>yd</p><p>06 </p><p>1216,1when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningmaximum a is 11 ,</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningminimum a is 53 ,</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningminimum a is 53 ,</p><p>0 occur when inflection of points Possible2</p><p>2</p><p>dx</p><p>yd</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningminimum a is 53 ,</p><p>0 occur when inflection of points Possible2</p><p>2</p><p>dx</p><p>yd</p><p>0126 .. xei</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningminimum a is 53 ,</p><p>0 occur when inflection of points Possible2</p><p>2</p><p>dx</p><p>yd</p><p>0126 .. xei</p><p>2x</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningminimum a is 53 ,</p><p>0 occur when inflection of points Possible2</p><p>2</p><p>dx</p><p>yd</p><p>0126 .. xei</p><p>2x</p><p>06,2when 3</p><p>3</p><p>dx</p><p>ydx</p></li><li><p>06 </p><p>1236,3when 2</p><p>2</p><p>dx</p><p>ydx</p><p> point turningminimum a is 53 ,</p><p>0 occur when inflection of points Possible2</p><p>2</p><p>dx</p><p>yd</p><p>0126 .. xei</p><p>2x</p><p>06,2when 3</p><p>3</p><p>dx</p><p>ydx</p><p> inflection ofpoint a is 32 ,</p></li><li><p>x </p><p>y </p></li><li><p>x </p><p>y </p><p> 11 ,</p></li><li><p>x </p><p>y </p><p> 11 ,</p><p> 53 ,5</p></li><li><p>x </p><p>y </p><p> 11 ,</p><p> 53 ,</p><p> 32 ,</p></li><li><p>x </p><p>y </p><p> 11 ,</p><p> 53 ,</p><p> 32 ,</p><p>5</p></li><li><p>x </p><p>y </p><p> 11 ,</p><p>596 23 xxxy</p><p> 53 ,</p><p> 32 ,</p><p>5</p></li><li><p>x </p><p>y </p><p> 11 ,</p><p>596 23 xxxy</p><p> 53 ,</p><p> 32 ,</p><p>5</p><p>Exercise 10F; </p><p>1bdf, 2, 4b, </p><p>5ace etc, 6bd </p><p>Exercise 10G </p><p>1, 2ace, 4b, 5c </p></li></ul>