Given the problem in the attachment, I am unsure about how to utilize the given information to evaluate the limit as x approaches 0.
\(\displaystyle \mbox{2. If I define the functions }\, f(x)\, \mbox{ and }\, h(x)\, \mbox{ as:}\)
. . . .\(\displaystyle f(x)\, =\, x^3\, +\, x^2\, -\, 5x\, -\, 2\)
. . . .\(\displaystyle h(x)\, =\, \dfrac{f(x)}{g(x)}\)
\(\displaystyle \mbox{...then evaluate:}\)
. . . .\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 0}\, \bigg(3\, h(x)\, +\, f(x)\, -\, 2\, g(x) \bigg)\)
\(\displaystyle \mbox{...under the following assumptions:}\)
. . . .\(\displaystyle \mbox{a. }\, h(x)\, \mbox{ is continuous for everywhere except }\, x\, =\, 2\)
. . . .\(\displaystyle \mbox{b. }\, \)\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, \infty}\, h(x)\, =\, \infty\)
. . . .\(\displaystyle \mbox{c. }\, \)\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 2}\, h(x)\, =\, \)\(\displaystyle \dfrac{1}{3}\)
If someone could help me with this problem it would be greatly appreciated.
\(\displaystyle \mbox{2. If I define the functions }\, f(x)\, \mbox{ and }\, h(x)\, \mbox{ as:}\)
. . . .\(\displaystyle f(x)\, =\, x^3\, +\, x^2\, -\, 5x\, -\, 2\)
. . . .\(\displaystyle h(x)\, =\, \dfrac{f(x)}{g(x)}\)
\(\displaystyle \mbox{...then evaluate:}\)
. . . .\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 0}\, \bigg(3\, h(x)\, +\, f(x)\, -\, 2\, g(x) \bigg)\)
\(\displaystyle \mbox{...under the following assumptions:}\)
. . . .\(\displaystyle \mbox{a. }\, h(x)\, \mbox{ is continuous for everywhere except }\, x\, =\, 2\)
. . . .\(\displaystyle \mbox{b. }\, \)\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, \infty}\, h(x)\, =\, \infty\)
. . . .\(\displaystyle \mbox{c. }\, \)\(\displaystyle \displaystyle \lim_{x\, \rightarrow\, 2}\, h(x)\, =\, \)\(\displaystyle \dfrac{1}{3}\)
If someone could help me with this problem it would be greatly appreciated.
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