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iykyk

Keats Mackay Englisch 51 Karten

iykyk

Karten in diesem Stapel (51)

  1. 1—n, 1/n, upper/lower - (normal - changed)/nn, 1/n, upper/lower - (normal - changed)/n
  2. 2—Prove that the dot product equals 1 as -1^n if n is odd then its -1 meant det(m) = -det(m) -> this is only true for 0.
    Because of this its either infinite or no solutions. For infinite the dot product must be zero which is show in the given maple output, implying that the vectors are perpendicular    Prove that the dot product equals 1 as -1^n if n is odd then its -1 meant det(m) = -det(m) -> this is only true for 0. Because of this...
  3. 3—Circle can only have two points colinear -> therefore there is no circle where this is trueCircle can only have two points colinear -> therefore there is no circle where this is true
  4. 4—Scalar triple product to prove they are on the plane (if it = 0) -> do all the combinations. If this is the case then they all lay within the sphere but within a circle (on the same plane). Therefore there are infinetely many spheres that could contain this circleScalar triple product to prove they are on the plane (if it = 0) -> do all the combinations. If this is the case then they all lay wit...
  5. 5—MTMMTM
  6. 6—exp(angle*I). Add 1 for the second one. This si because of vector addition we can add the two
    Last we just have to find the area of the parallelogram -> magntitude of cross product of the two vectors either side * the amount of points    exp(angle*I). Add 1 for the second one. This si because of vector addition we can add the two Last we just have to find the area of the p...
  7. 7—Area either side cancels out -> an odd function essentially thats been shifted of half the number -> think of it as another function that has been shifted. The integral has also been shifted should be -a a rather than -a + number/half a + number/halfArea either side cancels out -> an odd function essentially thats been shifted of half the number -> think of it as another functio...
  8. 8—InvertibleInvertible
  9. 9—Cant let any the bracket factorisastions tings equal 0 -> this will fuck leading columns otherwise and create parametersCant let any the bracket factorisastions tings equal 0 -> this will fuck leading columns otherwise and create parameters
  10. 10—Number at the top of vector.
    Obious bc if we made another function that made this 0 then we would have a polynomial with more 'roots' than degrees    Number at the top of vector. Obious bc if we made another function that made this 0 then we would have a polynomial with more 'roots' tha...
  11. 11—
  12. 12—
  13. 13—Left + ZX invert
    Expand out to get    Left + ZX invert Expand out to get
  14. 14—
  15. 15—Flipped sign of constant (expand out if need to into one fraction to work out) and multiply by constant in denominator (in brackets)
    If it equals that -> can compare 1/x^2 which diverges
    Otherwise it would be 1/x    Flipped sign of constant (expand out if need to into one fraction to work out) and multiply by constant in denominator (in brackets) If i...
  16. 16—* ln(x)* ln(x)
  17. 17—Maple
    Continuous
    exp(Answer for the one above)    Maple Continuous exp(Answer for the one above)
  18. 18—1-1 -> Polynomial so continuous and no turning points
    Solve for input
    Swap x and y and solve for y and then find the derivative and sub
    the coefficient on the RHS multiplied by the answer above    1-1 -> Polynomial so continuous and no turning points Solve for input Swap x and y and solve for y and then find the derivative and su...
  19. 19—-(answer of first) - (answer of second)
    Split into two different integrals and integrate by parts on both
    Two parts are each function times sin    -(answer of first) - (answer of second) Split into two different integrals and integrate by parts on both Two parts are each function tim...
  20. 20—Double the x=
    Not differentiable as its not continuous -> show that they approach different numbers    Double the x= Not differentiable as its not continuous -> show that they approach different numbers
  21. 21—Get all the differences between vectors and the parallel ones clearly have the same middle value. You may have to multiple by -1 to make same
    Use projection -> draw it out
    Both of them calculate the area of the parllelogram    Get all the differences between vectors and the parallel ones clearly have the same middle value. You may have to multiple by -1 to make ...
  22. 22—Both = 1
    This is because the cross products calculate the area of parallelogram so we do not need to multiply    Both = 1 This is because the cross products calculate the area of parallelogram so we do not need to multiply
  23. 23—Flips over the real axis
    Because inverse v = conj v if thats true -> if we add I and conj I it equals a real number
    Change the shit in the ^2 to that times its conj instead and then if in maple you get mod v remember its 1    Flips over the real axis Because inverse v = conj v if thats true -> if we add I and conj I it equals a real number Change the shit in...
  24. 24—
  25. 25—
  26. 26—A Plane + empty set
    Number each vector
    X1 + t1(X2-X1) + t2(X3-X1)    A Plane + empty set Number each vector X1 + t1(X2-X1) + t2(X3-X1)
  27. 27—First and last
    Eg (j and n)    First and last Eg (j and n)
  28. 28—Because A*lamba = U
    A*AT*Lamba = AT*U
    Therefore we can find the multiplicative difference    Because A*lamba = U A*AT*Lamba = AT*U Therefore we can find the multiplicative differenceBecause A*lamba = U A*AT*Lamba = AT*U Therefore we can find the multiplicative difference
  29. 29—Do substitution just remmeber to make the limits equal tan(original), or whatever the given equation isDo substitution just remmeber to make the limits equal tan(original), or whatever the given equation is
  30. 30—Pi -> sub value in to sin/cos and work around that
    infinity -> just make the numerator grow faster
    0 -> see what sin and cos equal at that value    Pi -> sub value in to sin/cos and work around that infinity -> just make the numerator grow faster 0 -> see what sin and cos equ...
  31. 31—beta - numerator * p
    P + 1
    Use the MVT between X and X + 1 remember to sub into C    beta - numerator * p P + 1 Use the MVT between X and X + 1 remember to sub into C
  32. 32—Write that becase I3 is LESS THAN what we got for the previous question: it converges for P>0Write that becase I3 is LESS THAN what we got for the previous question: it converges for P>0
  33. 33—Do implicit differentiation and should be clear that the constant on the top makes it bigger than 1 and is never undefined as the bottom is never zero due to coshDo implicit differentiation and should be clear that the constant on the top makes it bigger than 1 and is never undefined as the bottom ...Do implicit differentiation and should be clear that the constant on the top makes it bigger than 1 and is never undefined as the bottom ...
  34. 34—Split function theorem (differentiability + continuous)
    When we are at x=... we know the bottom equals 0, so should the top and so we can solve for that in the top. THen find the derivative of the top at 1 and then solve for the bottom.    Split function theorem (differentiability + continuous) When we are at x=... we know the bottom equals 0, so should the top and so we can...
  35. 35—AG = G - A = scalar * normal
    Should be some scalar of the normal
    Work this out for each x y and z and plug back into equation to find t
    Then sub back fro the worked out x y and z
    eg x = 3+4t -> sub that into equation    AG = G - A = scalar * normal Should be some scalar of the normal Work this out for each x y and z and plug back into equation to find t T...
  36. 36—OA - AG = R
    Sub R back into original equation and use the answer as the RHS instead    OA - AG = R Sub R back into original equation and use the answer as the RHS instead
  37. 37—The one with the real number eg 5^11
    Add on 2*Pi/ to the r (which can be seen as 5) and use the conversion    The one with the real number eg 5^11 Add on 2*Pi/ to the r (which can be seen as 5) and use the conversion
  38. 38—
  39. 39—The two that make m thingo 0
    The other one is the one that doesnt have a twin    The two that make m thingo 0 The other one is the one that doesnt have a twinThe two that make m thingo 0 The other one is the one that doesnt have a twin
  40. 40—Get M5 and divide bottom row by m shit
    Then solve each row as each variable is
    X Y Z A B C    Get M5 and divide bottom row by m shit Then solve each row as each variable is X Y Z A B C
  41. 41—First range - [<1 + val * -1], infinity)
    Eg. 20 -> -21
    b.i. -> take inside alpha divided constant of bottom
    eg. ln(x+9)/5    First range - [&lt;1 + val * -1], infinity) Eg. 20 -&gt; -21 b.i. -&gt; take inside alpha divided constant of bottom eg. ln(x+9)/5
  42. 42—Denominator m + 1 (eg 6)
    (6, infinity)
    Open interval to infinity    Denominator m + 1 (eg 6) (6, infinity) Open interval to infinity
  43. 43—1/2 * Pi, -1/2 * Pi, 3/4 * Pi, -3/4*Pi
    [0, infinity)
    Exponent(<4 or whatever value> * l)
    2 * Pi * /    1/2 * Pi, -1/2 * Pi, 3/4 * Pi, -3/4*Pi [0, infinity) Exponent(&lt;4 or whatever value&gt; * l) 2 * Pi * /
  44. 44—Rememebr that r and theta are times next to I in the exponent -> use conversion
    Remember first principle
    -(a+b*I) for last    Rememebr that r and theta are times next to I in the exponent -&gt; use conversion Remember first principle -(a+b*I) for last
  45. 45—
  46. 46—Paramters for function on each row
    Use these as values for mean value theorem    Paramters for function on each row Use these as values for mean value theorem
  47. 47—ALL
    Just infinite
    Determinant of A cannot = 0
    As Cx has infinite solutions -> det(A) = det(B) * det(C) = 0    ALL Just infinite Determinant of A cannot = 0 As Cx has infinite solutions -&gt; det(A) = det(B) * det(C) = 0
  48. 48—Increasing as the diff can never be zero -> look at output
    Add them = ln(1) which equals 0 -> therefore odd if you
    f(-x) + f(x) = 0
    f(-x) = -f(x)    Increasing as the diff can never be zero -&gt; look at output Add them = ln(1) which equals 0 -&gt; therefore odd if you f(-x) + f(x) = 0...
  49. 49—If FALSE => skey-smmetric & invertible
    first is the same
    second is ^rows * det(A)
    eg (-4)^18 * 39    If FALSE =&gt; skey-smmetric &amp; invertible first is the same second is ^rows * det(A) eg (-4)^18 * 39
  50. 50—A is the last row of the first matrix
    B is always 1    A is the last row of the first matrix B is always 1
  51. 51—Bottom Left of matrix B (could make same row) Plus the two values that make k shit 0
    <0, 0, 1> -> try and calculate anyways    Bottom Left of matrix B (could make same row) Plus the two values that make k shit 0 &lt;0, 0, 1&gt; -&gt; try and calculate anyways

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Karteikarten am iykyk, erstellt von Keats Mackay am 03/05/2023.
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