Why did French officials try to restrict settlement to the St. Lawrence Valley? They worried that a larger colony would be too hard to defend. They were required to do so by law. They wanted to wait until Quebec and Montreal were well established before expanding further. France and England had signed a treaty limiting French expansion.

\( \frac{dy}{dx}=\frac{x-y+5}{x+y-1} \)

4. If \( x x=\frac{5-\sqrt{21}}{2} \) then find i) \( x+\frac{1}{x} \)

\( \lim _{x \rightarrow 0} (\frac{1+x^{2}2^{x}}{1+x^{2}5^{x}})^{\frac{1}{\sin ^{3}x}} \)

II. USE THE REMAINDER THEOREM TO FIND THE REMAINDER WHENTHE GNEN POLYNOMIALISDINIEO GY EACH POIYNOMIAL. 1. \( P(x)=x^{3}-7 x+5 \div(x-1) \) 2. \( P(x)=2 x^{3}-7 x+3 \div(x+1) \) 3. \( P(x)=4 x^{4}-3 x^{3}-x^{2}+2 x+5 \div(x-2) \) 4. \( P(x)=2 x^{4}-3 x^{3}+4 x^{2}+17 x+7 \div(x-1) \) 5. \( P(x)=8 x^{4}+12 x^{3}+10 x^{2}+3 x+27 \div(2 x-3 \)

Biét dãy só \( \left(a_{n}\right) \) có \( a_{1}=1, a_{2}=2 \) và \( a_{n+2}=3 a_{n+1}+2 a_{n} \) vói moi in nguyên duong. Tìm \( a_{n} \) ?