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Chapter 1: Q. 46 (page 88)

Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
$\lim_{x \to \infty} (3 e^{- 2 x} + 1)$

Short Answer

Expert verified

The value is $1 .$

Step by step solution

01

Step 1. Given information.

The given function is $\lim_{x \to \infty} (3 e^{- 2 x} + 1) .$

02

Step 2. Value of the limit.

The table is,

The value approaches to $1$ as $x$ increases,

Therefore,

$\lim_{x \to \infty} (3 e^{- 2 x} + 1) = 1$ .

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Most popular questions from this chapter

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

$\lim_{x \to - 6} (x + 2) = - 4$ .

Write each of the inequalities in interval notation:

$|(3 x + 1) - 2| < 0.1$

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\lim_{x \to - 5} (3 x - 2) .$

Each function in Exercises 9–12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

$\lim_{x \to 0^{-}} f (x) = - 1, \lim_{x \to 0^{+}} f (x) = 1, f (0) = 0 .$

Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point $x = c$ .

$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 1$

See all solutions

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