What are the strengths and limitations of the Doppler and transit methods? What kinds of planets are easiest to detect with each method? Are there certain planets that each method cannot detect, even if the planets are very large? Explain. What advantages are gained if a planet can be detected by both methods?

Yes, there are certain planet that are not detected even if they are large.

Explanation:

The Doppler method is the radial-velocity method, and also an indirect method finding the extra solar planets and the brown dwarfs. While the transit method is a phenomenon only the celestial bodies are directly between a large body and an observer body. However, the transit method of the transiting planet is low as it depends on the alignment of the three objects that are in a near perfect straight line patterns. And that of the Doppler method that it can only measure movements along that line of sight, and this depends on the estimates of inclination of the planet's orbit to determine its mass. Thus of a planet is found by both these methods we can find its density, and an indication of its composition.