random

Question 1

differentiate a^(x)

Answer 1

a^(x)ln(a)

Question 2

why might the Newton-Raphson method fail?

Answer 2

if f’(x)=0 then the tangent is vertical and values won’t converge (to meet a root)

Question 3

how to integrate parametric equations

Answer 3

int[(y)(dx/dt)]dt

FIND NEW LIMITS (sub in x values to find t limits)

Question 4

differentiate parametric equations

Answer 4

dy/dx = (dy/dt)(dt/dx)

Question 5

how would you split up 30Σr=13 [(-2)^(r)-4r-78]?

Answer 5

• split into:
  30Σr=1 [(-2)^(r)-4r-78] - 12Σr=1 [(-2)^(r)-4r-78]
• split further into arithmetic and geometric sequences:
  30Σr=1 [(-2)^(r)] - 30Σr=1[4r+78]
  and
  12Σr=1 [(-2)^(r)] - 12Σr=1 [4r+78]

Question 6

what is the equation of the line in the MIDDLE of two parallel lines:
5x + 3y = 15
5x + 3y = 83

Answer 6

5x + 3y = 49

Question 7

how can a more accurate approximation be found using the Newton-Raphson method?

Answer 7

use more iterations

Question 8

volume of a sphere formula

Answer 8

V = (4/3)πr³

Question 9

how could you work out the value of k for a function where x≠k?

Answer 9

• usually at an assymptote
• if the function is a fraction, make the denominator equal to zero and solve to find out what value x cannot be
  (if x is this value, the function would be undefined)