(A) Find the Slope of the Tangent Line to the Curve

question 12

Essay

(a) Find the slope of the tangent line to the curve $y = x - \frac { 1 } { x } \text { at } ( 1,0 )$ (i)
using Definition 1 from Section 2.6.(ii)
using Definition 2 from Section 2.6.(b) Using your results from part (a), find an equation of the tangent line at (1, 0).

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Definitions:

Case Study

An in-depth exploration of a particular subject, group, or situation over a period of time, often used in psychological, sociological, and educational research to gather detailed insights.

Representative Subset

A portion of a larger group or data set that accurately reflects the characteristics or distribution of the whole.

Entire Group

Refers to the totality of members within a specified set or collection without exception.

Random Sample

A sample selected from a larger population in such a way that each member has an equal chance of being included, enhancing representativeness.