Tutor profile: Samantha F.
How do you write a good first paragraph?
Different types of writing need to focus on different things. The process for writing a good first paragraph for a literary essay versus for a short story is different. For an essay, your first paragraph is essentially the thesis or abstract of your paper. It is the ideas and themes explored within the paper condensed into one paragraph. It is good to start with a rather general statement that has relation to the themes of your essay. This statement should also be interesting and unique, rather than a simple summary of plot or something like that. Then take that idea and narrow it down until you reach the specifics of your essay and state your thesis. This is called a top down approach. For a short story, you want to focus on the emotional resonance and central idea of your story. What is the overarching plot and story arc happening? Is your piece character driven or plot driven? Is it a happy or sad piece? Your first paragraph should take these things into consideration and evoke the most important aspect of your story. It should introduce the central ideas of your story but also have some further draw, a point of intrigue that will make your reader want to read more. Your first paragraph should capture the fundamental essence of your story.
How do you show that a function is continuous?
A function is continuous at a point if the limit exists, and the limit as x goes to x-naught equals f(x-naught). In other words, the limit must be the same and exist when approaching from both directions in a 2D function and from all points in the open set (all paths) for a 3D function. To solve a limit and see whether or not that is true, start by simply plugging in the value of x-naught. If that doesn't work, substitute the paths x=0, y=0, x= my and solve. If that still yields nothing, try factoring or using the limit product rule. Finally, try testing different paths and seeing if each path gets the same answer. if none of those things works, then conclude that the limit does not exist.
How do you create lighting effects in a drawing in photoshop?
It depends on the type of piece you're creating. if you're painting digitally, you can simply paint in the lighting effects as you're working by adding highlights and shadows based on your chosen light source. Alternatively, a somewhat easier solution that would apply to cel-shaded pieces would be to use different layer effects on photoshop. You would create a new layer on top of your flat colors and change that layer moe to be Overlay (or a different setting depending on the kind of lighting effect you're going for). Overlay is a very versatile mode. Then using whatever brush you prefer, choose a darker purple or brown and paint on that layer. Paint shadows onto your piece as you wish. The overlay layer will darken where you paint without losing the original color. If the colors are still too intense, lower the opacity of the Overlay layer. You can also make the overlay layer (and any other layer effects) a clipping group to your base colors so that it will only paint where there has already been color.
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