a) Write down the definition of the derivative in terms of limits. Using this definition find (x² – 2x). d dx
a) Write down the definition of the derivative in terms of limits. Using this definition find (x² – 2x). d dx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![a) Write down the definition of the derivative in terms of limits. Using this definition find
(x² – 2x).
b)
d
dr
i) The definite integral can be defined as: [ f(x) dx = lim f(x)Ar. Explain, with
n→∞
the aid of a diagram, precisely what the symbols n, x and Ax mean.
ii) Consider a curve y = f(x) on the interval [a, b]. Derive, with the aid of a clear diagram,
a formula for the length of the curve between x = a and x = b.
c) By setting up a suitable integral, find the volume of a pyramid which has a square base of
side length L and height h.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96f0bd94-2e15-4b18-bfe0-7958c1b8a791%2F26c45b40-b242-4c63-86e6-0fa393f1a14f%2Fsg4ndfi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Write down the definition of the derivative in terms of limits. Using this definition find
(x² – 2x).
b)
d
dr
i) The definite integral can be defined as: [ f(x) dx = lim f(x)Ar. Explain, with
n→∞
the aid of a diagram, precisely what the symbols n, x and Ax mean.
ii) Consider a curve y = f(x) on the interval [a, b]. Derive, with the aid of a clear diagram,
a formula for the length of the curve between x = a and x = b.
c) By setting up a suitable integral, find the volume of a pyramid which has a square base of
side length L and height h.
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