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solve the following recurrence relations
a. 𝑇(𝑛) = 𝑇( 𝑛/4) + 𝑇( 𝑛/2 ) + 𝑛^2
b. T(n) = T(n/5) + T(4n/5) + n
c. 𝑇(𝑛) = 3𝑇( n/4 ) + 𝑐𝑛^2
f. 𝑇(𝑛) = (𝑛/𝑛−5) * 𝑇(𝑛 − 1) + 1
g. 𝑇(𝑛) = 𝑇(log 𝑛) + log 𝑛
h. 𝑇(𝑛) = 𝑇 (𝑛^ 1/ 4) + 1
i. 𝑇(𝑛) = 𝑛 + 7 √𝑛 ∙ 𝑇(√𝑛)
j. 𝑇(𝑛) = 𝑇 ( 3𝑛/4 ) + 1/root(n)
Find the limit superior and the limit inferior of the following sequences
a) {(1 +
1
𝑛
)
𝑛+1
}
b) {
(−1)
𝑛
𝑛2
}
Define a relation R on {a,b,c, int i* e . a Reflexive but not symmetric ↳ Symmetric but not transitive <> Transitive but not reflexive
Find the area between y=x^2 and x+y-2=0
Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation.
Express V= 2t² + 5t + 9 as a linear combination of the polynomials
P1= t + 1
P2= t - 1
P3 = t² - 2t + 1
A wall "h" meters high is 2m away from the building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6m. How high is the wall in meters?
The joint probability density function 𝑓(𝑥,𝑦) for the random variables 𝑋 and 𝑌 is defined as follows
𝑓(𝑥,𝑦)= 3/2
Are the random variables 𝑋 and 𝑌 independent?
Define a relation - on the set of real numbers by
x-ymeans I x | + I y I : I x+y l.
which of the properties for an equivalence relation does - satisfy?
Find the equation of the curve at every point that passes through the point (0, −1) and which the normal line at any point (x, y) has a slope of 1/(3x + 2).
