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The phrase "for the first example" is correct and can be used in written English.
This phrase is typically used when providing a series of examples or when introducing the first example in a list. Example: "There are many different types of marketing strategies, for the first example, let's discuss social media advertising."
Exact(35)
For the first example look at the BBC, where its multiple outlets – TV, radio, the web – are increasingly well-integrated: its TV and radio journalism feeds into web pages, while TV programmes are available again on the iPlayer, and radio is spread around the world over the net.
I turn to the restaurant Fraîche for the first example in this short blog series because it was at Fraîche that I heard one of my all-time favorite songs, a haunting, simple, gorgeous track by Bjork, "Unravel," that didn't make her greatest-hits collection and seems to fly under many Bjork lovers' radar.
The solutions for the first example are compared with the experimental results.
For the first example, we select the case in which (Omega= 0,1)^{2}).
For the first example, consider the two-link system depicted in Figure 1a.
For the first example it is shown that it is not possible to design a stable stabilizing controller.
Similar(24)
The first example is for analysis stratified by gender (26).
Parameter studies based on globally optimal solutions are carried out for the second example.
For the second example, we examine the recovery of a discontinuous coefficient using the adjoint method.
The data related to the part demand for the third example is given in Table 10.
For the second example, we consider a nonhomogeneous Dirichlet boundary problem.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com