Chapter 1: Q. 99 (page 137)

Use the quotient rule for limits and the continuity of $\cos x$ to prove that $f (x) = s e c x$ is continuous on its domain.

Short Answer

Expert verified

It is proved that $f (x) = s e c x$ is continuous on its domain.

Step by step solution

Step 1. Given Information

We are given that $\cos x$ is continous.

Step 2. Proving the statement

If $x = c$ is in the domain of $\sec x$ , then c is not a multiple of $\frac{π}{2}$ , and $\cos c \neq 0$ . Therefore, $\lim_{x \to c} \sec x = \lim_{x \to c} \frac{1}{\cos x}$ is the quotient of $\lim_{x \to c} 1$ by,

$\lim_{x \to c} \cos x = \cos c$

$\frac{1}{\cos c} = \sec c$

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Use the quotient rule for limits and the continuity of $\cos x$ to prove that $f (x) = s e c x$ is continuous on its domain.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the statement

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Use the quotient rule for limits and the continuity of cosxto prove that f(x)=secxis continuous on its domain.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proving the statement

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Use the quotient rule for limits and the continuity of $\cos x$ to prove that $f (x) = s e c x$ is continuous on its domain.