Doubt

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

Synopsis
L, in a bid to profile Light's behavior, challenges him to a game of tennis, with both having previously been tennis champions (L being one in Britain), only to quit. 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 attempts wins the match (typical of a sore loser, which L suspects Kira is), then he must be Kira; simultaneously 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". As the whole school watches the match, an opportunity is found, and Light takes it by slamming the tennis ball underneath L's racket, declaring Light the winner 6 sets to 4.

Afterwards, L asks him some questions regarding the Kira case, and if he would be willing to help in the Kira investigation, even revealing that Light is a suspect. They go to a coffee shop of Light's suggestion, where L shows him the notes from the prisoner experiments. Light solves the puzzle of "L DO YOU KNOW GODS OF DEATH LOVE APPLES?", but L pulls a scam by showing Light a fake fourth note and changing the meaning of the message to "L DO YOU KNOW GODS OF DEATH WHO LOVE APPLES HAVE RED HANDS?", claiming that Light should have thought that there might be a fourth note, even if there wasn't one. Light reacts defensively, raising L's suspicions.

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, while Soichiro reveals to Light that L is, in fact, who he says he is. 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, and saying that if they do not broadcast them, everyone in the company will die; eager for a new story, the head of the company greedily agrees.

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.