Please capitalize where necessary: the problem was to determine the resultant vibration produced by all the wavelets reaching any point behind the diffracter.
A: The problem was to determine the resultant vibration produced by all the wavelets reaching any point behind the diffracter.

Q: in fact, despite writing a work which appears to us today to be in the style of a modern textbook, grassmann failed to convince mathematicians of his own time.

A: In fact, despite writing a work which appears to us today to be in the style of a modern textbook, Grassmann failed to convince mathematicians of his own time.

Q: in order to prevent this disease, it is recommended that you not expose your dog to kennel like or boarding conditions, where large populations of dogs are contained and mixed together. however, if you cannot avoid this, then a proper vaccination would be the best option.
A: In order to prevent this disease, it is recommended that you not expose your dog to kennel like or boarding conditions, where large populations of dogs are contained and mixed together. However, if you cannot avoid this, then a proper vaccination would be the best option.

Problem: adam did not believe what god told him face to face.
Can you repeat this sentence, but capitalize it?
Answer: Adam did not believe what God told him face to face.

Text: he pored over the old testament and found it was but a code that cleared before his eyes.

Correct capitalization: He pored over the Old Testament and found it was but a code that cleared before his eyes.

Text: and sent them to proclaim the kingdom of god and to heal the sick.

Correct capitalization:
and sent them to proclaim the kingdom of God and to heal the sick.