Undertake, v. t. [imp. Undertook; p. p. Undertaken; p. pr. & vb. n. Undertaking.]
Etymology: [Under + take.]
1. To take upon one's self; to engage in; to enter upon; to take in hand; to begin to perform; to set about; to attempt. To second, or oppose, or undertake The perilous attempt. Milton.
2. Specifically, to take upon one's self solemnly or expressly; to lay one's self under obligation, or to enter into stipulations, to perform or to execute; to covenant; to contract. I 'll undertake to land them on our coast. Shak.
3. Hence, to guarantee; to promise; to affirm. And he was not right fat, I undertake. Dryden. And those two counties I will undertake Your grace shall well and quietly enjoiy. Shak. I dare undertake they will not lose their labor. Woodward.
4. To assume, as a character. [Obs.] Shak.
3 more senses
5. To engage with; to attack. [Obs.] It is not fit your lordship should undertake every companion that you give offense to. Shak.
6. To have knowledge of; to hear. [Obs.] Spenser.
7. To take or have the charge of. [Obs.] "Who undertakes you to your end." Shak. Keep well those that ye undertake. Chaucer.
1 other Webster entry under this spelling
Undertake, v. i.
1. To take upon one's self, or assume, any business, duty, or province. O Lord, I am oppressed; undertake for me. Isa. xxxviii. 14.
2. To venture; to hazard. [Obs.] It is the cowish terror of his spirit That dare not undertake. Shak.
3. To give a promise or guarantee; to be surety. But on mine honor dare I undertake For good lord Titus' innocence in all. Shak.
Shades of meaning
Fernald has no entry of its own for undertake; he lists it under endeavor.
Where he writes about it:
To undertake is to accept or take upon oneself as an obligation, as some business, labor, or trust; the word often implies complete assurance of success; as, I will undertake to produce the witness. — from endeavor