Question

Assume lim f(x)-6 and lim g(x)-9. Compute the following limit and state the limit laws used to justify the computation.
x→3 x →3

Lim 3√f(x).g(x)+10
x →3

Answer 1

Answer:

4

Step-by-step explanation:

some relevant limit laws

lim C = C where c is a constant.

lim( f(x)  + g(x)) =lim f(x) + lim g(x)

lim( f(x)g(x)) =lim f(x) * lim g(x)

lim( cg(x)) =clim g(x)

lim( f(x)/g(x)) =lim f(x) / lim g(x) if  lim g(x) is not equal to zero.

lim( f(x))^2 = (lim f(x) )^2

lim  square root( f(x)) = square root(lim f(x) )

$\lim_{n \to 3} g(x) = 9\\\\\lim_{n \to 3} f(x) = 6\\\\ \lim_{n \to 3} \sqrt[3]{f(x)g(x) + 10} \\\\ = \lim_{n \to 3} \sqrt[3]{f(x)g(x) + 10}\\\\= \sqrt[3]{lim_{n \to 3}f(x) \times lim_{n \to 3}g(x) + 10}\\\\= \sqrt[3]{6 \times 9 + 10}\\\\= \sqrt[3]{64}$

= 4