The graph of f(x) is shown. f(x) = 4x x2+9 (a) Find the following limi

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The graph of f(x) is shown. f(x) = 4x x2+9 (a) Find the following limits. L = limx→+∞ f(x) = K = limx→−∞ f(x) = (b) Determine x1 and x2 in terms of ε. x1 = x2 = (c) Determine M, where M > 0, such that |f(x)−L| < ε for x > M. M = (d) Determine N, where N < 0, such that |f(x)−K| < ε for x < N. N =

The graph of f(x) is shown. f(x) = 4x x2+9 (a) Find the following limits. L = limx→+∞ f(x) = K = limx→−∞ f(x) = (b) Determine x1 and x2 in terms of ε. x1 = x2 = (c) Determine M, where M > 0, such that |f(x)−L| < ε for x > M. M = (d) Determine N, where N < 0, such that |f(x)−K| < ε for x < N. N =

Image text

The graph of

f (x)

is shown.

f (x) = \frac{4 x}{\sqrt{x^{2} + 9}}

(a) Find the following limits.

\begin{array}{l} L = lim_{x \to + \infty} f (x) = \\ K = lim_{x \to - \infty} f (x) = \end{array}

◻

◻

(b) Determine

x_{1}

and

x_{2}

in terms of

ε

.

\begin{array}{l} x_{1} = ◻ \\ x_{2} = ◻ \end{array}

(c) Determine

M

, where

M > 0

, such that

| f (x) - L | < ε

for

x > M

.

M = ◻

(d) Determine

N

, where

N < 0

, such that

| f (x) - K | < ε

for

x < N

.

N = ◻

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