Oblicz granicę Natalia: Oblicz granicę: lim x→∞(sin√x+1−sin√x)

Mariusz: sin(A+B)=sin(A)cos(B)+cos(A)sin(B) sin(A−B)=sin(A)cos(B)−cos(A)sin(B) sin(A+B)−sin(A−B)=(sin(A)cos(B)+cos(A)sin(B))−(sin(A)cos(B)−cos(A)sin(B)) sin(A+B)−sin(A−B)=2cos(A)sin(B) A+B=√x+1 A−B=√x 2A=√x+1+√x 2B=√x+1−√x

	√x+1+√x		√x+1−√x
sin(√x+1)−sin(√x)=2cos(		)sin(		)
	2		2

	√x+1+√x		x+1−x
2cos(		)sin(		)
	2		2(√x+1+√x)

	√x+1+√x		1
2cos(		)sin(		)
	2		2(√x+1+√x)

cosinus jest ograniczony a sinus dąży do zera