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LM2623: Boost converter for Li-Ion Battery

Part Number: LM2623
Other Parts Discussed in Thread: TPS61230A

Hello dear TI,

I am building one project, where I need boost converter, that can gives me 2 A at 5 Volts. 

I found that IC LM2623 should gives me that 2 A, but in datasheet I found graph:

So can I ask you if it really can gives me 2 A (or at least 1 A) if on its input is 1 Li-Ion cell (input voltage = from 3 V to 4.2 V).

Regards,

Ondrej Bures