Show that the function is continuous on R. f: R→ R, f(x)= 1 Show that f given in 2b) is intergrable and fő f (x) dx = 2 In 2 = = ∞ n=1 sin (nx) Σ n² n=1 Let 08< be given. Show that f given in 2b) is differentiable at each x € (8,27 - 6). Find f' (T). Hint: Use the following formula n=1 1 (2n - 1)³ (−1)n- n

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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Please answer all the questions to show continuity, differentiability and that it is reimann integrable thanks

 

2b.
2c.
2d.
Show that the function
is continuous on R.
ƒ: R→ R, f(x)
1
Show that f given in 2b) is intergrable and
* f (x) da = 2
In 2 =
=
n=1
∞
2Σ
n=1
n=1
Let 0 < d < π be given. Show that f given in 2b) is differentiable at each x € (8, 2π – 8).
Find f' (T).
Hint: Use the following formula
sin (nx)
n²
1
(2n − 1)³
n
Transcribed Image Text:2b. 2c. 2d. Show that the function is continuous on R. ƒ: R→ R, f(x) 1 Show that f given in 2b) is intergrable and * f (x) da = 2 In 2 = = n=1 ∞ 2Σ n=1 n=1 Let 0 < d < π be given. Show that f given in 2b) is differentiable at each x € (8, 2π – 8). Find f' (T). Hint: Use the following formula sin (nx) n² 1 (2n − 1)³ n
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