Whoever knows Me as the Supreme Personality of Godhead, without doubting, is the knower of everything. He therefore engages himself in full devotional service to Me, O son of Bharata.
(Bhagavad-Gita-----15:9-----translation).

Two words used in this verse to address the Supreme Lord—Hṛṣīkeśa and Keśi-niṣūdana—are significant. Hṛṣīkeśa is Kṛṣṇa, the master of all senses, who can always help us attain mental serenity. Arjuna requests Him to summarize everything in such a way that he can remain equipoised. Yet he has some doubts, and doubts are always compared to demons. He therefore addresses Kṛṣṇa as Keśi-niṣūdana. Keśi was a most formidable demon who was killed by the Lord; now Arjuna is expecting Kṛṣṇa to kill the demon of doubt.
(Bhagavad-Gita-----18:1-----translation).

A person in Kṛṣṇa consciousness or in the mode of goodness does not hate anyone or anything which troubles his body. He does work in the proper place and at the proper time without fearing the troublesome effects of his duty. Such a person situated in transcendence should be understood to be most intelligent and beyond all doubts in his activities.
(Bhagavad-Gita-----18:10-----purport).

Śukadeva Gosvāmī was speaking to Mahārāja Parīkṣit about the activities of King Priyavrata, and since the King might have had doubts about these wonderful, uncommon activities, Śukadeva Gosvāmī reassured him. "My dear King," he said, "don't be doubtful about the wonderful activities of Priyavrata. For a devotee of the Supreme Personality of Godhead, everything is possible because the Lord is also known as Urukrama." Urukrama is a name for Lord Vāmanadeva, who performed the wonderful act of occupying the three worlds with three footsteps. Lord Vāmanadeva requested three paces of land from Mahārāja Bali, and when Mahārāja Bali agreed to grant them, the Lord immediately covered the entire world with two footsteps, and for His third step He placed His foot upon Bali Mahārāja's head.
(Srimad Bhagavatam-----5:1:35-----purport).

Āryans do not deviate from the instructions of Kṛṣṇa, nor do they have doubts about Kṛṣṇa, but non-Āryans and other demoniac people fail to follow the instructions of Bhagavad-gītā and Śrīmad-Bhāgavatam. This is because they have been trained in sense gratification at the cost of all other living entities. Nūnaṁ pramattaḥ kurute vikarma: (S.B.5:5:4) their only business is to indulge in all kinds of forbidden activities for sense gratification. Yad indriya-prītaya āpṛṇoti: they deviate in this way because they want to gratify their senses. They have no other occupation or ambition. Their method of civilization is condemned in the previous verse. Kaḥ kṣemo nija-parayoḥ kiyān vārthaḥ sva-para-druhā dharmeṇa: "What is the meaning of a civilization that kills oneself and others?"
(Srimad Bhagavatam-----6:16:43-----purport).

In Bhagavad-gītā the word asaṁśaya is used to describe the devotee. There the Lord Himself gives this instruction:
mayy āsakta-manāḥ pārtha
yogaṁ yuñjan mad-āśrayaḥ
asaṁśayaṁ samagraṁ māṁ
yathā jñāsyasi tac chṛṇu
"Now hear, O son of Pṛthā (Arjuna), how by practicing yoga in full consciousness of Me, with mind attached to Me, you can know Me in full, free from doubt." (B.G.7:1)
(Srimad Bhagavatam-----9:9:42-----purport).

It is natural for the Lord to be untinged by material qualities, and because everything is perfectly present in His spiritual energy, as soon as He desires something, it is immediately done. The Lord is not a prākṛta-śiśu, a child of this world, but by His personal energy He appeared like one. Ordinary people may have difficulty accepting the supreme controller, God, as a human being because they forget that He can do everything by spiritual energy (ātma-māyayā). Nonbelievers say, "How can the supreme controller descend as an ordinary being?" This sort of thinking is materialistic. Śrīla Jīva Gosvāmī says that unless we accept the energy of the Supreme Personality of Godhead as inconceivable, beyond the conception of our words and mind, we cannot understand the Supreme Lord. Those who doubt that the Supreme Personality of Godhead can come as a human being and turn Himself into a human child are fools who think that Kṛṣṇa's body is material, that He is born and that He therefore also dies.
(Srimad Bhagavatam-----10:3:46-----purport).

By such transcendental knowledge of the all-pervading Personality of Godhead, one is able to see the Absolute Truth everywhere. Freed thus from all doubts, one gives up fruitive activities.
(Srimad Bhagavatam-----11:29:18-----translation).

Although the sky, or space, is the resting place of everything, the sky does not mix with anything, nor is it entangled. Similarly, the sun is not at all attached to the water in which it is reflected within innumerable reservoirs, and the mighty wind blowing everywhere is not affected by the innumerable aromas and atmospheres through which it passes. In the same way, a self-realized soul is completely detached from the material body and the material world around it. He is like a person who has awakened and arisen from a dream. With expert vision sharpened by detachment, the self-realized soul cuts all doubts to pieces through knowledge of the self and completely withdraws his consciousness from the expansion of material variety.
(Srimad Bhagavatam-----11:11:12-13-----translation).