Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Concept explainers
Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Question

Transcribed Image Text:The instantaneous slope of f(x)
when f(x) is radical
10
6,sqrt(26))
1.0
F10
1,0
10
-10
f(x) = V3x + 8
%3D
compute the instantaneous slope at: (6, v26)
Start with two points
A : (6, v26) and B : (6+ h, ?)
What is the y-coordinate of B?
• Because the x-coordinate of B depends on h, the y-coordinate will also
depend on h.
Compute Ax and Ay
Compute and Reduce Ax/Ay
Finding the limit
Use the steps above to compute the instantaneous rate of change for f(x) at
(6, v26), then use your answer to find an equation for the line tangent to f(x) at
(6, /26):
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