"File: Secant"

"AUXILIARY FUNCITONS"

E_(y,a):=ITERATE(y,x,a,1)

L_(y,a,b):=(x-a)*(E_(y,b)-E_(y,a))/(b-a)+E_(y,a)

LS_(y,a,h,n):=VECTOR(L_(y,a,a+h*k),k,n,1,-1)

S_(y,a,h,n):=[y,LS_(y,a,h,n)]

"####################################"

"USER FUNCTIONS"

SECANT(y,a,h,n):=S_(y,a,h,n)

"#########################################"

"INSTRUCTIONS"

"SECANT(y,a,h,n) produces a picture of y=f(x) together with secant lines"

"through (a,y(a)) and (a+kh,y(a+kh)) as k ranges from 1 to n."

"ApproX SECANT(Y,A,H,N) and Plot."

"##########################################"

"Example"

"approX and then Plot the following to see secant lines"

"to y=sin x at a=0"

SECANT(SIN(x),0,0.4,5)