Daily Graph 23-02-09

y=(e^x-e^-x)/2
dy/dx = (e^x+e^-x)/2 which is always positive
d²y/dx²=(e^x-e^-x)/2 which is positive when x>0 and negative when x<0.
at x=0,y=0

addition here also

division of graphs... [4]

red one is required graph... in above post

y=(e^x - e^-x)/ (e^x + e^-x)
dy/dx = 4/(e^x+e^-x)² which is >0
d²y/dx² = -8(e^x-e^-x)/(e^x+e^-x) which is >0 when x<0 and <0 when x>0
At x=0,y=0
But as x increases or decreases...... e^x+e^-x becomes very large..... hence at large values of x, slope becomes almost zero...

lines after large valus of x are almost straight

gr8 priyam and mee same graphs although i like his method better [3]

e^x=cosx+isinx
e^-x=cosx-isinx
add........cosx=y1 sinx=y2 and y3=tanx

so........shud i hav 2 draw d graph now???????

yikes...........sorry.......didnt see tht

nishant bhiayya, are priyam's and my graphs for y=(e^x-e^-x)/2 wrong??

i think u r rite...ashis..[1]..[12]