Question

Given that limx→−1f(x)=5 and limx→−1g(x)=−1, evaluate the following.

limx→−1(f(x)⋅g(x))

(If the limit does not exist, enter ∅.)

Answer 1

lim x→-1 f(x)g(x)=(5)(-1)=-5, product of the limits

Example: f(x)=(x²+7x+6)/(1+x), g(x)=(x²+x)/(1+x); so f(x)g(x)=(x⁴+8x³+13x²+6x)/(1+x)². 

lim x→-1 f(x) = 5 and lim x→-1 g(x) = -1 (because denominator is a factor of the numerator)

lim x➝-1 (x⁴+8x³+13x²+6x)/(1+x)²=-5, because denominator is a factor of the numerator and f(x)g(x) reduces to x²+6x (for x≠-1), which has the value -5 when x=-1.