menu
bartleby
search
close search
Hit Return to see all results

(b) Deduce the result of part a an alternative way by showing that for any m xn matrix A, we have1/2| Ax|

Question

Please help me problem 8a. Thanks!

(b) Deduce the result of part a an alternative way by showing that for any m xn matrix A, we have
1/2
| Ax| <(Σα)
i,j
8. Using Theorem 3.2 whenever possible (and standard facts from one-variable calculus), decide in
each case whether lim f (x) exists. Provide appropriate justification.
XO
()
()
C)
0-0
x2 y
X
xy
X
(a) f
(f) f
= 0
X
x +y+1
X
sin (x2y2)
x3
X
(b) f
(g) f
x2y2
x2 - y2
sin2
x
X
Xx
X
y
(c) f
xy, f
(h) f
X
1
xy
x2 y2
X
xy
X
X
(d) f
exty2
(i) f
= 0
1
X
3-y3 y, f
Xr
X
()-
()
x2 +y2
()-
X
X
(e) f
= e-1/(r2+y2)
(j) f
x# -y, f
= 0
y
x + y
9. Suppose f: R" R" is continuous and xo is arbitrary. Define a sequence by xk f(x-1),
k = 1, 2, .... Prove that if x a, then f(a) = a. We say a is a fixed point off.
10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it
exists.
1
help_outline

Image Transcriptionclose

(b) Deduce the result of part a an alternative way by showing that for any m xn matrix A, we have 1/2 | Ax| <(Σα) i,j 8. Using Theorem 3.2 whenever possible (and standard facts from one-variable calculus), decide in each case whether lim f (x) exists. Provide appropriate justification. XO () () C) 0-0 x2 y X xy X (a) f (f) f = 0 X x +y+1 X sin (x2y2) x3 X (b) f (g) f x2y2 x2 - y2 sin2 x X Xx X y (c) f xy, f (h) f X 1 xy x2 y2 X xy X X (d) f exty2 (i) f = 0 1 X 3-y3 y, f Xr X ()- () x2 +y2 ()- X X (e) f = e-1/(r2+y2) (j) f x# -y, f = 0 y x + y 9. Suppose f: R" R" is continuous and xo is arbitrary. Define a sequence by xk f(x-1), k = 1, 2, .... Prove that if x a, then f(a) = a. We say a is a fixed point off. 10. Use Exercise 9 to find the limit of each of the following sequences of points in R, presuming it exists. 1

fullscreen
check_circleAnswer
Step 1

Consider the fu...

ху
x y
help_outline

Image Transcriptionclose

ху x y

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Limits

Sorry about that. What wasn’t helpful?