Evaluate the limit: limħ– →0 0-2 01/1/20 0 - 12/1/2 2 an ( 7 +h)-tan (7) h

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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Evaluate the limit: \(\lim_{{h \to 0}} \frac{{\tan\left(\frac{\pi}{4} + h\right) - \tan\left(\frac{\pi}{4}\right)}}{h}\)

Options:
- ○ \(-2\)
- ○ \(\frac{1}{2}\)
- ○ \(-\frac{1}{2}\)
- ● \(2\) (Correct answer)
Transcribed Image Text:Evaluate the limit: \(\lim_{{h \to 0}} \frac{{\tan\left(\frac{\pi}{4} + h\right) - \tan\left(\frac{\pi}{4}\right)}}{h}\) Options: - ○ \(-2\) - ○ \(\frac{1}{2}\) - ○ \(-\frac{1}{2}\) - ● \(2\) (Correct answer)
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Step 1: Given problem

We space have space to space evaluate space the space limit colon
space limit as straight h rightwards arrow 0 of fraction numerator tan open parentheses straight pi over 4 plus straight h close parentheses minus tan open parentheses straight pi over 4 close parentheses over denominator straight h end fraction

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