英文翻译。.我相信你可以的,希望你不会让我失望。

I know you can do it. Hope you won't disappoint me.

这个语境下know可以表达更强烈的可能性，会令对方听了更舒服一点。

换一个语境就不一样了，比如你朋友担心自己某个考试过不了，为了鼓励他你可以说 I believe you can pass the exam. 也可以说I know you can pass the exam. 但是这里却是believe比较好，用know会太强烈，毕竟你又不是批卷老师怎么知道他会不会过。但是如果是在他考试通过以后则应该说I know (重音) u can pass it. 表示“看吧，我就说你可以过的”

I'm sure you can,hope that you won't let me down.

I believe you can make it. Come on, don't let me down!

I think you can do it well,don't let me upset.

I have faith in you. I expect you won't let me down! ^_^