the questions are via attachment can you please solve both questions.

 

 

Mathematics IB Assignment 4
Semester 2, 2016
Submit solutions by 2pm Monday 5th September
(together with solutions for Assignment 5)
Algebra
Let
u1 = (1, 0, 1, 0), u2 = (0, 2, 0, 1), u3 = (1, 2, 1, 0) and let W be the subspace of R4 with basis {u1 , u2 , u3 }.
Use the Gram–Schmidt process to find an orthonormal basis for W .
You must show all your working. Calculus
Evaluate the following limits using only techniques from sections 2.12.6 of the lecture notes (i.e. not L’Hopital’s Rule), showing details of
your working.



1 1
1
(a) lim
+
x→−3 x
3
x3 − 9x
tan 5x
(b) lim 2
x→0 3x + 7x 1

Attachments:

• 1492649710-1.pdf