CALCULUS

34 flashcards · Other · by Minh Đức

1. what is a function f of x

   asign each element of x in a set D only 1 element in set E

2. property of vertical line test

   cut the curve of a function only once

3. what is an odd function

   f(-x) = -f(x)

4. what is an even function

   f(-x) = f(x)

5. what is domain

   set of possible values of x

6. what is range

   set of possible values of y

7. how to check a 1 to 1 function

   use horizontal line check, it must cross only once

8. f-1(y) = x => f(x) = y

9. suppose y() is inverse of g(), domain of y() is A, range of y() is B so domain ofg() is B, range of g() is A

10. how can we obtain graph of f-1(x)

    reflect graph of f(x) through y = x

11. 4 steps to find inverse function

    write f(x) = y solve x in terms of y replace y and x now y = ...... is inverse function

12. what is the domain and range of ln(u) domain: u>0 range:-inf,inf

13. what is the domain of cos(t)

    -inf,inf

14. y = ax + b what is the slope and what does it represent

    slope is a: it represents for the additional value of y for each value that x increments

15. y = ax + b , what is the y- intercept

    b

16. formular of the tangent line of y = f(x)

    y = y'(x0) * (x-x0) + y0

17. how to find instantaneous velocity at a point by using graph

    we find the slope at that point, by using 2 points infront and before that point

18. (a-b)^3 =

    a^3 - 3a^2. b + 3a.b^2 - b^3

19. a^3 + b^3 =

    (a+b) * (a^2 - ab + b^2)

20. a^3 - b^3 =

    (a-b) (a^2 + ab + b^2)

21. how to find average velocity on time(a,b)

    s(b) - s(a) / b - a

22. how to find instantaneous velocity at a

    s'(a) = v(a)

23. how to prove f is differentiable

    f is continuous f'(x) exists at that point

24. tangent line at a point => ........ tangent line through a point => .....

    x0,y0 x,y

25. lim ( sin x / x ) =

    1

26. lim ( cos x - 1) / x =

    0

27. (sin-1(x) )' = ?

    1/sqrt(1-x2)

28. (cos-1(x) )' = ?

    -1/sqrt(1-x2)

29. (tan-1(x) )' = ?

    1/(1+x2)

30. csc(x) = csc(x) ' =

    1/sin(x) -csc(x) . cot(x)

31. sec(x) = sec(x) ' =

    1/cos(x) sec(x). tan(x)

32. tan(x) ' =

    sec(x)^2

33. cot(x) ' =

    -csc(x)^2

34. | u |' =

    u' * u / |u|