Doubt

Doubt  (疑う, Utagau) is the tenth episode in the Death Note (anime).

Synopsis
L, in a bid to profile Light's behavior, challenges him to a game of tennis. During the game, they question in their thoughts regarding whether if Kira is Light and if L is really L. L determines that if Light wins the match, then he must be Kira; then again if he purposely loses the match (to not create suspicion) he could be Kira also.

Light determines that if he wins the match then L would assume that Light is Kira, so he aims to lose the match to not create suspicion. At the same time, they think that in order to get confirmation that their identities are true, they'll "have to go to Task Force headquarters". An opportunity is found, and Light takes it by slamming the tennis ball underneath L's racket, declaring Light the winner. Afterwards, L asks him some questions regarding the Kira case, and if he would be willing to help in the Kira investigation.

The two then receive news that Soichiro Yagami has had a heart attack and is in hospital. Light promises an oath to his father that he will make sure Kira is caught and executed for making him suffer. On the way out, L confronts and scrutinizes Light, still uncertain if he is or is not Kira. Light attempts another bluff and demands to be placed in a prison cell without television for one month to prove his innocence. For now L is satisfied but curious that Light offers this proposition. Meanwhile a television station, Sakura TV, receives audio tapes from an anonymous person claiming to be Kira.

Goofs
in their tennis match, the scene where L's arm is near his face (the sky is in the background), the arm of his shirt has become short sleeved, in the next scene it is back to being long sleeved again.