1 - If you are using Bootstrap with the default Grid you theoretically would need the images in these resolutions. Here is the official documentation: https://getbootstrap.com/docs/4.0/layout/grid/
$grid-breakpoints: (
// Extra small screen / phone
xs: 0,
// Small screen / phone
sm: 576px,
// Medium screen / tablet
md: 768px,
// Large screen / desktop
lg: 992px,
// Extra large screen / wide desktop
xl: 1200px
);
2 - To load the images in the slider with each of the grid resolutions you can do Srcset as Valdeir commented. That way your image would look something like this:
<picture>
<source media="(min-width: 576px)" srcset="suaimagem-sm.png" sizes="100vw"/>
<source media="(min-width: 768px)" srcset="suaimagem-md.png" sizes="100vw"/>
<source media="(min-width: 992px)" srcset="suaimagem-lg.png" sizes="100vw"/>
<source media="(min-width: 1200px)" srcset="suaimagem-lx.png" sizes="100vw"/>
<picture>
This answer has a load test for you to see how Chrome Devtools requests the images on srcset
How best to work with responsive images?
Another way to treat the img tag would be like in this Mozilla article on responsive image https://developer.mozilla.org/en-US/docs/Aprender/HTML/Multimedia_and_embedding/Responsive_images
<img srcset="suaimagem-sm.png 576w,
suaimagem-md.png 768w,
suaimagem-lg.png 992w,
suaimagem-lx.png 1200w"
sizes="(max-width: 576px) 280px,
(max-width: 768px) 580px,
(max-width: 992px) 780px,
1200px"
src="suaimagem-lx.png" alt="">
srcset
https://developer.mozilla.org/en-US/docs/Web/HTML/Element/img#Specifications or https://developer.mozilla.org/en-US/docs/Web/HTML/Element/picture#Example_1_uso_com_attribute com_media to use multiple resolutions without browser load all images.– Valdeir Psr