G(x)= (x+1)(x+3)Q(x) + px +q
a) Given that G(x) leaves a remainder of 8 and −24 when divided by (x+1) and
(x+3) respectively,find the remainder when G(x) is divided by (x+1)(x+3).
b) Given that x+2 is a factor of G(x) and that the graph of G(x) passes through
the point with coordinates (0,6) find G(x)
Which of the series converge and
which diverge? Check by the limit
comparison test.
1) Σ_(n=2) ^∞ ((1+n ln(n))/(n^2 +5))
2) Σ_(n=1) ^∞ ((ln(n))/n^(3/2) )
3) Σ_(n=3) ^∞ (1/(ln(lnn)))
4) Σ_(n=1) ^∞ (1/(n (n)^(1/n) ))
??
Find the third degree polynomial which vanishes when
x =−1 and x = 2, which has a value 8 when x =0 and leaves a remainder ((16)/3) when
divided by 3x + 2.
solve for real x and y:[a,b∈R]
a. { ((x^3 +1=y^3 )),((x^2 +1=y^2 )) :}
b. { ((x^3 +x^2 +1=y^3 )),((x^2 +x+1=y^2 )) :}
c. { ((x^3 +y^2 =9xy)),((x^2 +y^3 =8xy)) :}
d. { ((ax+by=2ab)),((x^2 +y^2 =4abxy)) :}