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Assignment 1 3

This tutorial letter for MAT1613 Calculus B includes important information regarding Assignment 1, which covers topics such as related rates, graphs of functions, rates of change, optimization, and L'Hôpital's rule. The assignment consists of four questions with a total of 50 marks, and has a fixed closing date of May 10, 2024. Specific tasks include determining asymptotes, analyzing function behavior, and applying L'Hôpital's rule to various limits.

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antique dube
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62 views2 pages

Assignment 1 3

This tutorial letter for MAT1613 Calculus B includes important information regarding Assignment 1, which covers topics such as related rates, graphs of functions, rates of change, optimization, and L'Hôpital's rule. The assignment consists of four questions with a total of 50 marks, and has a fixed closing date of May 10, 2024. Specific tasks include determining asymptotes, analyzing function behavior, and applying L'Hôpital's rule to various limits.

Uploaded by

antique dube
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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MAT1613/102/0/2024

Tutorial Letter 102/0/2024

CALCULUS B

MAT1613

Year module

Department of Mathematical Sciences

IMPORTANT INFORMATION:
This tutorial letter contains questions
to assignment 01.

BAR CODE

university
Define tommorow. of south africa
MAT1613

ASSIGNMENT 1

2024
′
(Related Rates, Graphs of functions, rates of change, optimization, L Hôpital’s rule)

FIXED CLOSING DATE: 10 May 2024

Question 1 [20 Marks]


x
Let f (x) = (x−1)2

(a) Determine the horizontal and vertical asymptotes. (4)


′
(b) Use the sign pattern for f (x) to determine

(i) the interval(s) over which f rises and where it falls. (5)
(ii) the local extrema. (2)
′′
(c) Use the sign pattern for f (x) to determine

(i) where the graph of f is concave up and where it is concave down. (5)
(ii) the inflection points (if any) (4)

Question 2 [8 Marks]

The volume of a cube is increasing at a rate of 1200cm3 /min at the moment the lengths of the sides
are 20cm. How fast are the lengths of the sides increasing at that moment? (8)

Question 3 [4 Marks]
√ 
Find the exact value of cos(tan−1 −4 3 ). (4)

Question 4 [18Marks]
′
Use L Hôpital’s rule to determine
cos x−1+2x 2
(a) lim 2x 2
(5)
x→0

1
− x1
 
(b) lim ex −1 (6)
x→0

(c) lim (1 + 4x)cot x (7)


x→0+

Total Marks = 50

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