Calculus studies change by analyzing slopes of secant lines over

allhvasstH

allhvasstH

Answered question

2021-10-04

Calculus studies change by analyzing slopes of secant lines over successively shorter intervals.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

Answer & Explanation

firmablogF

firmablogF

Skilled2021-10-05Added 92 answers

Given statement is 'Calculus studies change by analysing slopes of secant lines over succesively shorter intervals'
This sentence makes send because this is one of the topic of Calculus subject.
This is one of the calculus subject's topics, so this sentence makes sense.
To approximate the slope of the tangent line to the function graph at that particular point, find the secant line slopes over progressively shorter intervals.
The slope of secant line on interval [a, a+h] is,
f(a+h)f(a)h
The slope tangent line can be approximates by the slope of secant line by making h smaller and smaller. That means to find the slopes of secant line successively over the shorter intervals for smaller values of h.
Therefore, the slope of tangent line m at point (a, f(a)) is
m=limh0f(a+h)f(a)h

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