Part(i). Discuss Continuous and Discontinuous functions? Also construct a table of at least four ordered pairs of points on the graph of the given functions and also sketch the graph of function (using excel) a) 3×3 + 9×2 -6 b) 4×2 – 9x +2 c) 2×3- 9 Part ii) Discuss in detail Fundamental theorem of Calculus and also evaluate the following integrals (Make sure u are showing works in details)
a) ∫√(𝟐𝒙𝟐 −𝟒)3 dx b) ∫ 𝒔𝒊𝒏𝟐(𝒙) 𝟏 +𝒔𝒊𝒏𝟐(𝒙) 𝟐 𝟎 𝒅𝒙
Part iii) What is the Vertical line test and Horizontal line test? What are their applications shows with graphs?
Part iv) Discuss briefly Product and Quotient Rule of Differentiation and also differentiate the following functions. a) (4×3−x)(10−20x) b) (4t2−t)(t3−8t2+12) c) (5×2/x3 +3)
Discuss in detail sequence and Series? Consider the sequence -12,-7,
-2, 3, ………Is it athematic? If so, Find thirty-second term of A.P and use sum formula to find 87st term in the sequence..
Word limit: 1000 to 1200 Expectations:
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1. Please choose only one of the two questions. You will be panelized for doing both.
2. Submit your answer paper in an academic format, with proper introduction, body, conclusion and references.