f ( x )= a*ebx , x>0
g(x) = sin(x)+1 , x<0
An der Nahtstelle müßte gelten
f ( x ) = g ( x )
und
f ´ ( x ) = g ´( x )
f ´ ( x ) = a * e^{bx} * b
f ´ ( x ) = ab * e^{bx}
g ´ ( x ) = cos(x)
g ( 0 ) = 1
g ´( 0 ) = 1
f ( 0 ) = a* e^{b*0} = 1
f ´( 0 ) = ab * e^{b*0} = 1
=> b = 1
a* e^{1*0} = 1
a * 1 = 1
a = 1
f ( x ) = e^x , x ≥ 0
g ( x ) = sin ( x ) + 1 < 0
Wo hast du die blaßblaue Textfarbe her ?
(x) = sin(x)+1 , x<0