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What methods are used to detect planets around distant stars?

Answer 1

Direct observation
Transit method mostly by Kepler space telescope.
Wobbling action of star when planet comes near to ,it in orbit. Doppler spectroscopy).
gravitational lensing.

Only very few planets were observed by this method.
Majority of Exo planets were detected b y this method (Transit).

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Answer 2

Emma Arguello

Planets around far-off stars can be found using a variety of techniques, such as the following: 1. Transit method; 2. Radial velocity method; 3. Direct imaging; 4. Gravitational microlensing; 5. Astrometry

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.