Differential Calculus, Cheat Sheet of Calculus

Differential Calculus topics on trigonometric and exponential functions

Typology: Cheat Sheet

2020/2021

Uploaded on 10/25/2021

Erwin_Rommel
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EXERCISE 2.1 Trigonometric, Exponential and Logarithmic Functions
A. Evaluate the following trigonometric functions:
1. ๐‘๐‘œ๐‘ (7๐œ‹
6) and ๐‘๐‘œ๐‘ (โˆ’7๐œ‹
6)
2. ๐‘ก๐‘Ž๐‘›(โˆ’๐œ‹
4) and ๐‘ก๐‘Ž๐‘›(7๐œ‹
4)
3. ๐‘ ๐‘’๐‘(25๐œ‹
6)
4. ๐‘๐‘œ๐‘ (2๐œ‹)
B. Sketch the graph of the exponential functions
5. โ„Ž(๐‘ก)= 2 โˆ’ 4๐‘’๐‘ก4
โ„
6. โ„Ž(๐‘ก)= 1 โˆ’ 4๐‘’1โˆ’๐‘ก 4
โ„
C. Give the exact value of the following logarithms:
7. ๐‘™๐‘œ๐‘”23 = 1
8. ๐‘™๐‘œ๐‘”2โˆš32
7
D. Evaluate the following expressions:
9. ๐‘™๐‘›๐‘ฅ3๐‘ฆ4๐‘ง5
10. ๐‘™๐‘œ๐‘”(4๐‘ฅ3+ ๐‘ฆ)

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EXERCISE 2 .1 Trigonometric, Exponential and Logarithmic Functions

A. Evaluate the following trigonometric functions:

7 ๐œ‹

6

) and ๐‘๐‘œ๐‘  (โˆ’

7 ๐œ‹

6

๐œ‹

4

) and ๐‘ก๐‘Ž๐‘› (

7 ๐œ‹

4

25 ๐œ‹

6

B. Sketch the graph of the exponential functions

๐‘ก

4

โ„

1 โˆ’๐‘ก

4

โ„

C. Give the exact value of the following logarithms:

23

2

7

D. Evaluate the following expressions:

3

4

5

3