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The graphs of polar equations

XP 17 M152 / SP2021 / Bingham

Directions: Answer the questions posed below, submit your answers to CANVAS as a Written Submission (direct written entry into CANVAS, using CANVAS writing tools) or as a File Upload. This XP is worth a maximum of 10 points.

1a) The graphs of polar equations and have two points of intersection.
Identify those points using Polar coordinates AND rectangular coordinates.

1b) The graph of linear equation has two intercepts.
Identify those points using rectangular coordinates AND polar coordinates.
Then, write the original equation in Polar function form. (that’s form)

2a) Using your calculator/technology to help, sketch the graph of the Polar function
on a set of Polar axes.

Graph it over the interval ; mark the orientation of the graph.

Also, mark the positions and give the exact Polar coordinates of the points where

 .       (hint:  shows up a lot)

b) Find the Polar radial derivative for the function in part a. Then, use it to find the exact values of for the values mentioned in part a, above.
At which two points in part a’s graph does = 0?

Sample Solution

hand, is concerned with decayed emotion. An inconsistency in Gothic is that ‘Gothic novelists did not know how to release their own feelings of frustration and rebelliousness. Their fiction is both exploratory and fearful’ as Kilgour tells us. It usually results in the death of a villain. Miles has a valid point about how you cannot constrain Gothic to a particular type of text, preferring to class Gothic literature as a taste or preference. Overall, I will show that the reception of gothic writing-its institutional and commercial recognition as a kind of literature- played a fundamental role in shaping many of the ideological assumptions about high culture that we now associate with the term Romanticism. The Gothic novel was first invented almost single-handedly by Walpole as The Castle of Otranto fits most of the classifications we see in Gothic today. ‘The Gothic, like any genre, depends on a system of classification, and because genres, as Derrida argues, are never pure, and systems of classification, according to Foucault, cannot be verified, one is pressed to investigate and contest the validity of the definitions and conceptions typically attributed to the term “Gothic”, a kind of writing that is evidently heterogeneous and impure’ (Alshatti, A. (2008).). Walpole’s novel was imitated in the eighteenth century, but it was enjoyed widespread influence in the nineteenth century partly because of the era’s understanding in dark and fascinating themes. He could be said to have been influenced by Shakespearean dramas because in The Castle Of Otranto he plays around with mental disturbances, where Manfred seeks to marry the soon to be wife of his dead son Conrad to keep his genes alive throughout generations. Lady Macbeth evidently suffers from a psychotic disorder with the misfortune of hallucinations which can be induced by extreme guilt. She has the sense of heavy guilt because her and her husband killed King Duncan in cold blood. Gothic, it can be argued, was instrumental in the decisive shift towards popular fiction in its modern form, aimed at a brood readership, commercially streamlined, form
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