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Chapter 1: Q. 55 (page 136)

$\lim_{x \to π} \frac{1}{\cos e c (π - x)}$

Short Answer

Expert verified

$\lim_{x \to π} \frac{1}{\cos e c (π - x)} = 0$

Step by step solution

Step 1. Given information

$\lim_{x \to π} \frac{1}{\cos e c (π - x)}$

Step 2. Plug in the values

$If \lim_{x \to a -} f (x) = \lim_{x \to a +} f (x) = L then \lim_{x \to a} f (x) = L$

$\lim_{x \to π +} \frac{1}{\cos e c (π - x)} = 0$

$\lim_{x \to π -} \frac{1}{\cos e c (π - x)} = 0$

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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 $47 - 60$ .

$\lim_{x \to 3} (x^{2} - 6 x + 11) = 2$ .

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.

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

Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes.

Calculate each of the limits:

$\lim_{x \to 1} x \sin^{- 1} \frac{x}{2}$ .

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

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limx→π1cosec(π-x)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Plug in the values

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$\lim_{x \to π} \frac{1}{\cos e c (π - x)}$