When writing in a academic setting (think of a letter to your professor), what is the most appropriate way of saying this?
I will be grateful if you could resolve this doubt in your paper.
I will be grateful if you could dispel this doubt I have in you paper.
You can suggest better alternatives than those in the title.
Neither is correct in American English. As we use it, "doubt" is not a synonym of "question", and would never be used in these sentences. It generally implies a challenge to a statement, rather than an uncertainty. Both "resolve" and "dispel" could also be read as possibly implying a challenge in this context, since they imply that the problem is in the paper rather than in your understanding of it.
I think what you are trying to say is "I would be grateful if you could answer a question I have about your paper." (Also note the use of "would", to match "could", and "about" rather than "in".)
American English having such a diverse regional variation in usage of words, I do not find anything wrong with the sentence
I will be grateful if you could resolve this doubt in your paper.
In fact, having been in engineering practice, I have encountered the use of resolving a doubt with sufficient frequency.
Doubt is the foundation of quality engineering. We raise doubts. Raising doubts is a skill, as much as is resolving those doubts.
However, sometimes we find ourselves not having to resolve doubts but to resolve conflicts. They are not the same.
In management, financial and legal practice, people may find it expedient to discover and then resolve conflicts. But in engineering practice, one must always be adept at raising and resolving doubts.
For example, when we propose that there are 96% of rods produced fall within 3 ft +/- 0.2 inch, we would attempt to raise a doubt to test this theory, where the doubt says there are more than 4% of rods that lie beyond the specified range. When we find that the doubt is valid, we have to act to resolve this doubt by improving the process producing the rods.
We could also raise doubts in non-quantitative ways. A doubt could be raised about the presumptions made concerning an equation. A doubt could arise about the symmetry of one model with the actual situation on which we wish to apply that model. To resolve the doubt, we would need to discover as much as possible the dissimilarities between model and situation, and try to mitigate those dissimilarities.
Anyway, when it comes to application of technology, the raising and resolution of doubts are essential activities towards producing quality products.
