Evaluate the limit given the information

[jtstien]

Given the problem in the attachment, I am unsure about how to utilize the given information to evaluate the limit as x approaches 0.

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\(\displaystyle \mbox{2. If I define the functions }\, f(x)\, \mbox{ and }\, h(x)\, \mbox{ as:}\)

. . . .$\displaystyle f(x)\, =\, x^3\, +\, x^2\, -\, 5x\, -\, 2$

. . . .$\displaystyle h(x)\, =\, \dfrac{f(x)}{g(x)}$

\(\displaystyle \mbox{...then evaluate:}\)

. . . .$\displaystyle \displaystyle \lim_{x\, \rightarrow\, 0}\, \bigg(3\, h(x)\, +\, f(x)\, -\, 2\, g(x) \bigg)$

\(\displaystyle \mbox{...under the following assumptions:}\)

. . . .\(\displaystyle \mbox{a. }\, h(x)\, \mbox{ is continuous for everywhere except }\, x\, =\, 2\)

. . . .\(\displaystyle \mbox{b. }\, \)$\displaystyle \displaystyle \lim_{x\, \rightarrow\, \infty}\, h(x)\, =\, \infty$

. . . .\(\displaystyle \mbox{c. }\, \)$\displaystyle \displaystyle \lim_{x\, \rightarrow\, 2}\, h(x)\, =\,$$\displaystyle \dfrac{1}{3}$

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If someone could help me with this problem it would be greatly appreciated.