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f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

f(x) A B = arcsin x, then lim 1/1/12 0 ㅠ 6 f(x)−ƒ( ² ) X→ X- 1|2 is

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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If \( f(x) = \arcsin x \), then \[ \lim_{{x \to \frac{1}{2}}} \frac{f(x) - f\left(\frac{1}{2}\right)}{x - \frac{1}{2}} \] is A) \( 0 \) B) \( \frac{\pi}{6} \) C) \( \frac{2}{\sqrt{3}} \) D) nonexistent
Transcribed Image Text:If \( f(x) = \arcsin x \), then \[ \lim_{{x \to \frac{1}{2}}} \frac{f(x) - f\left(\frac{1}{2}\right)}{x - \frac{1}{2}} \] is A) \( 0 \) B) \( \frac{\pi}{6} \) C) \( \frac{2}{\sqrt{3}} \) D) nonexistent
The image presents a multiple-choice question about calculus, asking for the derivative of the inverse secant function, \(\sec^{-1} x\), with respect to \(x\). The provided options are: **A)** \(-\sin x\) **B)** \(\tan x \sec x\) **C)** \(\frac{1}{x^2 \sqrt{1 - \left(\frac{1}{x}\right)^2}}\) **D)** \(\frac{-1}{x^2 \sqrt{1 - \left(\frac{1}{x}\right)^2}}\) These options represent possible expressions for the derivative of \(\sec^{-1} x\).
Transcribed Image Text:The image presents a multiple-choice question about calculus, asking for the derivative of the inverse secant function, \(\sec^{-1} x\), with respect to \(x\). The provided options are: **A)** \(-\sin x\) **B)** \(\tan x \sec x\) **C)** \(\frac{1}{x^2 \sqrt{1 - \left(\frac{1}{x}\right)^2}}\) **D)** \(\frac{-1}{x^2 \sqrt{1 - \left(\frac{1}{x}\right)^2}}\) These options represent possible expressions for the derivative of \(\sec^{-1} x\).
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