Pick an amount for d_x, it has to be really small!
14
Expression 15: "d" Subscript, "x" , Baseline equals 0dx=0
00
0.10.1
15
Now below, divide the value of dy (shown on the graph) with the value of dx! That value is close to something...(You can also call on the value of dy by typing d_y)
16
Expression 17: StartFraction, "d" Subscript, "y" , Baseline Over "d" Subscript, "x" , Baseline , EndFractiondydx
undefined
17
Expression 18:
18
Expression 19: "y" equals "f" left parenthesis, "c" , right parenthesis left brace, "c" less than or equal to "x" less than or equal to "c" plus "d" Subscript, "x" , Baseline , right brace left brace, "v" equals 1 , right bracey=fcc≤x≤c+dxv=1
undefined
19
Expression 20: "x" equals "c" plus "d" Subscript, "x" , Baseline left brace, "f" left parenthesis, "c" , right parenthesis less than or equal to "y" less than or equal to "f" left parenthesis, "c" plus "d" Subscript, "x" , Baseline , right parenthesis , right brace left brace, "v" equals 1 , right bracex=c+dxfc≤y≤fc+dxv=1
undefined
20
Expression 21: "x" equals "c" plus "d" Subscript, "x" , Baseline left brace, "f" left parenthesis, "c" plus "d" Subscript, "x" , Baseline , right parenthesis less than or equal to "y" less than or equal to "f" left parenthesis, "c" , right parenthesis , right brace left brace, "v" equals 1 , right bracex=c+dxfc+dx≤y≤fcv=1
undefined
21
Expression 22: "f" left parenthesis, "x" , right parenthesis equals StartFraction, "x" cubed Over 2 , EndFraction minus "x" cosine "x" minus 2 "x" squared plus "x" sine left parenthesis, "x" squared , right parenthesisfx=x32−xcosx−2x2+xsinx2
22
dx = ${d_x} left parenthesis, "c" plus StartFraction, "d" Subscript, "x" , Baseline Over 2 , EndFraction , "f" left parenthesis, "c" , right parenthesis plus 0.0 0 2 , right parenthesis left brace, "v" equals 1 , right brace left brace, "d" Subscript, "x" , Baseline greater than 0 , right bracec+dx2,fc+0.002v=1dx>0
Label:
undefined
23
Expression 24: "q" equals "f" left parenthesis, "c" plus "d" Subscript, "x" , Baseline , right parenthesis minus "f" left parenthesis, "c" , right parenthesisq=fc+dx−fc
equals=
00
24
dy = ${q} left parenthesis, "c" plus "d" Subscript, "x" , Baseline , left parenthesis, StartFraction, "f" left parenthesis, "c" , right parenthesis plus "f" left parenthesis, "c" plus "d" Subscript, "x" , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis , right parenthesis left brace, "v" equals 1 , right brace left brace, "d" Subscript, "x" , Baseline greater than 0 , right bracec+dx,fc+fc+dx2v=1dx>0