Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the...

12
Sheet 1 13. (ii) 01 December 2020 22:33 Tutorial 2 Page 1

Transcript of Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the...

Page 1: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 1 13. (ii)01 December 2020 22:33

Tutorial 2 Page 1

Page 2: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Tutorial 2 Page 2

Page 3: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 1 1501 December 2020 22:33

Tutorial 2 Page 3

Page 4: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Tutorial 2 Page 4

Page 5: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 1 1801 December 2020 22:33

Tutorial 2 Page 5

Page 6: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Tutorial 2 Page 6

Page 7: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 1 Optional 701 December 2020 22:36

Tutorial 2 Page 7

Page 8: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Tutorial 2 Page 8

Page 9: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Tutorial 2 Page 9

Page 10: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 1 Optional 1001 December 2020 22:37

Tutorial 2 Page 10

Page 11: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 2 201 December 2020 22:37

Tutorial 2 Page 11

Page 12: Sheet 1 13. (ii) - GitHub Pages · 2020. 12. 30. · 13. (ii) Discuss the continuity of the following function. x sin . for 0 and f (0) 15. Let f (x) on IR. Is f' a continuous function?

Sheet 2 501 December 2020 22:38

Tutorial 2 Page 12


f x a an nx bn ( ) 0 cos (1) - t U · 1 1 Fourier Series Periodic Function A function is called “periodic” function of period p if f(x+np) = f(x), x, n >0, n: integer. If both

f x a an nx bn ( ) 0 cos (1) - t U · 1 1 Fourier Series Periodic Function A function is called “periodic” function of period p if f(x+np) = f(x), x, n >0, n: integer. If both

Derivative of any function f(x,y,z): Differential Calculus (revisited): Gradient of function f.

Derivative of any function f(x,y,z): Differential Calculus (revisited): Gradient of function f.

arithmetic function f n x ˇ n x ˇ von Mangoldt function

arithmetic function f n x ˇ n x ˇ von Mangoldt function

Assignment - PBworksdustintench.pbworks.com/f/GA1G10102.pdf · Functional Function: F of x it is! Functional Notation The function f(x) c 9__ 5 32 represents the temperature in degrees

Assignment - PBworksdustintench.pbworks.com/f/GA1G10102.pdf · Functional Function: F of x it is! Functional Notation The function f(x) c 9__ 5 32 represents the temperature in degrees

Let f be the function defined by : (a≠0) I - Algebraic properties : 1°) Even function : for any x R, f(-x) = f(x). 2°) Rate of growth not constant :

Let f be the function defined by : (a≠0) I - Algebraic properties : 1°) Even function : for any x R, f(-x) = f(x). 2°) Rate of growth not constant :

CCA 2014 - transcendentalarithmetic.nettranscendentalarithmetic.net/cca2014proceedings.pdf · spaces and f : X ! Y is a partial function, then a function F : !!! !! realizes f if

CCA 2014 - transcendentalarithmetic.nettranscendentalarithmetic.net/cca2014proceedings.pdf · spaces and f : X ! Y is a partial function, then a function F : !!! !! realizes f if

(1 )pongsak.ee.engr.tu.ac.th/le200/FourierTransformNote.pdf1 1 Fourier Series Periodic Function A function is called “periodic” function of period p if f(x+np) = f(x), x, n >0,

(1 )pongsak.ee.engr.tu.ac.th/le200/FourierTransformNote.pdf1 1 Fourier Series Periodic Function A function is called “periodic” function of period p if f(x+np) = f(x), x, n >0,

Chapter 3. Functions 3.1 What is a Function f x f x f x · Chapter 3. Functions 3.1 What is a Function Definition of Function A function f is a rule (or a set of rules) that assigns

Chapter 3. Functions 3.1 What is a Function f x f x f x · Chapter 3. Functions 3.1 What is a Function Definition of Function A function f is a rule (or a set of rules) that assigns

mrsstuckeysmathclass.weebly.com€¦ · Mixed Exercises 62. If function f multiplies x by 2, then r I by 2. Function f is defined byf(x) = f -1 is defined by f -I(x) = 64. Suppose

mrsstuckeysmathclass.weebly.com€¦ · Mixed Exercises 62. If function f multiplies x by 2, then r I by 2. Function f is defined byf(x) = f -1 is defined by f -I(x) = 64. Suppose

OPEL V1.1 Special Function · OPEL EUROPE 1997 Astra -F Engine X 18 XE X X X X Adjust Idle Speed . Mark Description X Function is supported. OPEL V1.1 . Mark Description X Function

OPEL V1.1 Special Function · OPEL EUROPE 1997 Astra -F Engine X 18 XE X X X X Adjust Idle Speed . Mark Description X Function is supported. OPEL V1.1 . Mark Description X Function

Definition of the derivative f’(x) of a function f(x) The ...pirate.shu.edu/~wachsmut/Teaching/MATH1401/2012-03/Exam1...2 4 ( ) 2 k x x x x f x 7. Prove that the function x3 4x 1

Definition of the derivative f’(x) of a function f(x) The ...pirate.shu.edu/~wachsmut/Teaching/MATH1401/2012-03/Exam1...2 4 ( ) 2 k x x x x f x 7. Prove that the function x3 4x 1

The composition function k(x) = (f o g)(x) = f (g(x)) g f g f R->[0,+oo)->[-1, 1]

The composition function k(x) = (f o g)(x) = f (g(x)) g f g f R->[0,+oo)->[-1, 1]

Key Concept Absolute Value Parent Function f x

Key Concept Absolute Value Parent Function f x

Estimation of the spectral density function. The spectral density function, f( ) The spectral density function, f(x), is a symmetric function defined.

Estimation of the spectral density function. The spectral density function, f( ) The spectral density function, f(x), is a symmetric function defined.

Distribution Function properties. Density Function – We define the derivative of the distribution function F X (x) as the probability density function.

Distribution Function properties. Density Function – We define the derivative of the distribution function F X (x) as the probability density function.

1.1 Relations and Functions 1. Relation: A set of ordered ... · 1. Function Notation: f(x), which is read “f of x.” Interpreted as the value of the function f at x. y f(x) indicated

1.1 Relations and Functions 1. Relation: A set of ordered ... · 1. Function Notation: f(x), which is read “f of x.” Interpreted as the value of the function f at x. y f(x) indicated

6.3 – GRAPHING SINE AND COSINE FUNCTIONS. Periodic Function and Period A function is periodic if, for some real number α, f(x + α) = f(x) for each x.

6.3 – GRAPHING SINE AND COSINE FUNCTIONS. Periodic Function and Period A function is periodic if, for some real number α, f(x + α) = f(x) for each x.

Slopes, Derivatives, and Tangentsshatalov/POWERPOINT FINALLLLLLLLLLpdf.pdfDerivatives of Functions ! For any function f(x), one can create another function f’(x) that will find the

Slopes, Derivatives, and Tangentsshatalov/POWERPOINT FINALLLLLLLLLLpdf.pdfDerivatives of Functions ! For any function f(x), one can create another function f’(x) that will find the

ExamView - Algebra 2 2.1-2.3 Worksheetrwright/algebra2... · Tell whether the function is linear. Then evaluate the function when x =−6. 8. f x()=3x +4 9. f x()=x3 −7 10. f x()=4+x

ExamView - Algebra 2 2.1-2.3 Worksheetrwright/algebra2... · Tell whether the function is linear. Then evaluate the function when x =−6. 8. f x()=3x +4 9. f x()=x3 −7 10. f x()=4+x

Graph each function: 1. f(x) = -2x 2 – 4x + 3 2. f(x) = -x 3 + 4x 2 1. 1.

Graph each function: 1. f(x) = -2x 2 – 4x + 3 2. f(x) = -x 3 + 4x 2 1. 1.