b If U = x + express x° + 1 m the form U + AU4 + BU² + C. State the values of A, B and C.
b If U = x + express x° + 1 m the form U + AU4 + BU² + C. State the values of A, B and C.
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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Need help with question 14b
![are non-zero real numbers. Prove that m² : n² = 10:3.
i x +
The coefficients of the terms in a' and a-3 in the expansion of |
FI
are in the ratio 2 : 1.
-3 in the expansion of (3x
12
coefficients
+
Hence find the values of a if these
13
та +
are equal, where m and n
4а Еxpand (х +
ENRICHMENT
b If U
= x +
express x
in the form U6 + AU4 + BU² + C. State the values of A, B and C.
15 a By starting with
h Find the term indendent of x in the expansion of (x + 1 + x-)*.
+ y) + z), expand (x + y + z).
16 [The Sierpinski triangle fractal]
a Draw an equilateral triangle of side length 1 unit on a piece of white paper. Join the midpoints of
the sides of this triangle to form a smaller triangle. Colour it black. Repeat this process on all white
triangles that remain. What do you notice?
b Draw up Pascal's triangle in the shape of an equilateral triangle, then colour all the even numbers
black and leave the odd numbers white. What do you notice? This pattern will be more evident it
take at least the first 16 rows
- perhaps use a computer program to generate 100 rows of Pascal
-
triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb267c5e5-56a0-40e3-b934-afb304f592bb%2Fa1db5b17-830b-427e-b362-cf8b9f0c986b%2Fz8jj2ub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:are non-zero real numbers. Prove that m² : n² = 10:3.
i x +
The coefficients of the terms in a' and a-3 in the expansion of |
FI
are in the ratio 2 : 1.
-3 in the expansion of (3x
12
coefficients
+
Hence find the values of a if these
13
та +
are equal, where m and n
4а Еxpand (х +
ENRICHMENT
b If U
= x +
express x
in the form U6 + AU4 + BU² + C. State the values of A, B and C.
15 a By starting with
h Find the term indendent of x in the expansion of (x + 1 + x-)*.
+ y) + z), expand (x + y + z).
16 [The Sierpinski triangle fractal]
a Draw an equilateral triangle of side length 1 unit on a piece of white paper. Join the midpoints of
the sides of this triangle to form a smaller triangle. Colour it black. Repeat this process on all white
triangles that remain. What do you notice?
b Draw up Pascal's triangle in the shape of an equilateral triangle, then colour all the even numbers
black and leave the odd numbers white. What do you notice? This pattern will be more evident it
take at least the first 16 rows
- perhaps use a computer program to generate 100 rows of Pascal
-
triangle.
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