'Despair' in the Bible

And David said in his heart, I shall now perish one day by the hand of Saul: there is nothing better for me than that I should speedily escape into the land of the Philistines; and Saul will despair of me to seek me any more within all the limits of Israel, and I shall escape out of his hand.

Then I went about to cause my heart to despair of all the labour wherewith I had laboured under the sun.

For we do not wish you to be ignorant, brethren, as to our tribulation which happened to us in Asia, that we were excessively pressed beyond our power, so as to despair even of living.