MAT1512 Latest exam pack questions and answers and summarized notes for exam preparation. Updated for October November 2023 exams . For assistance Whats-App.0.6.7..1.7.1..1.7.3.9 . All the best on your exams!!
MAT1613 Assignment 3 (COMPLETE ANSWERS) 2024 - DUE 20 September 2024
Summary/Cheat sheet for McGraw-Hill Ryerson Calculus & Advanced Functions
All for this textbook (3)
Written for
University of South Africa (Unisa)
Calculus A (MAT1512)
All documents for this subject (18)
Seller
Follow
iStudy
Reviews received
Content preview
MAT1512
EXAM PACK
FOR ASSISTANCE WITH THIS MODULE +27 67 171 1739
, 1 MAT1512
January /February 2023
UNIVERSITY EXAMINATIONS
January/February 2023
MAT1512
Calculus A
Examiners:
First: DR Z.I. ALI
Second: MR S. BLOSE
100 Marks
2 Hours
Closed book and online examination, which you have to write within 2 hours
and submit online through the link: https://myexams.unisa.ac.za/portal
Use of a non-programmable pocket calculator is NOT allowed
This web based examination remains the property of the University of South
Africa and may not be distributed from the Unisa platform.
This examination allows attachment documents only as part of your
submission.
Declaration: I have neither given nor received aid on this examination.
Answer All Questions and Submit within the stipulated timeframe.
Late submission will not be accepted.
This paper consists of 4 pages.
ALL CALCULATIONS MUST BE SHOWN.
[TURN OVER]
, 2 MAT1512
January /February 2023
QUESTION 1
(a) Determine the following limits (if they exist):
x 1 2x 1
(i) lim (3)
x 0 3x 4 2 x 4
(ii) lim
x
x 2
xx (3)
1 cos 3 x
(iii) lim (3)
x sin 2 x
sin 2 x
(iv) lim (2)
x 0 sin 3x
3x 2 6
(v) lim (2)
x 5 2x
(vi) lim
x
25x 2
x 5x (3)
(b) Use the Squeeze Theorem to determine the following limit:
x 2 x sin x
lim (3)
x x 2 cos x
(c) Consider the function f given below:
ax if x 1
f x x 2 a b if 1 x 1
bx if 1 x
(i) Determine the one-sided limits lim f x and lim f x . (2)
x 1 x 1
(ii) Find the one-sided limits lim f x and lim f x . (2)
x 1 x 1
(iii) Hence or otherwise determine the numerical values of a and b . (2)
[25]
, 3 MAT1512
January /February 2023
QUESTION 2
(a) Using the first principles of differentiation, find the first derivative of f x 3x 2
2
x
at x 1 . (5)
(b) Find the derivatives of the following functions by using the appropriate rules of
differentiation:
sin x cos x
(i) f x (3)
sin x cos x
(ii) g x e 4 x sin 4 x (3)
2 4
x x
(iii) F x tan t dt and G x t dt (5)
x x2
(c) The curve C has the equation
cos 2 x cos 3 y 1 , x , 0 y
4 4 6
dy
(i) Find in terms of x and y . (4)
dx
(ii) The point P lies on C where x .
6
Find the equation of the tangent to C at P , giving your answer in the form
ax by c 0
where a , b and c are integers. (5)
[25]
QUESTION 3
(a) Determine the following integrals:
x2 4
(i) x 2 dx (2)
sin x
(ii) 2 5 cos xdx (2)
1 cos x
(iii) x sin xdx (2)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller iStudy. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.76. You're not tied to anything after your purchase.
