Questions
MAT135H5_F25_ALL SECTIONS 4.2 Preparation Check
Multiple dropdown selections
Suppose you are asked to find the Linear Approximation of ๐ ( ๐ฅ ) = tan โก ๐ฅ at ๐ฅ = ๐ 4 . Remember that the Linear Approximation is given by: ๐ฟ ( ๐ฅ ) = ๐ ( ๐ ) + ๐ โฒ ( ๐ ) ( ๐ฅ โ ๐ ) ย (a) What is ๐ ( ๐ 4 ) ? [ Select ] 2/sqrt(3) 1 -1 0 1/sqrt(2) (b) What is ๐ โฒ ( ๐ฅ ) ? [ Select ] f'(x)= sec^2x f'(x)= tan x f'(x) = sec x tan x f'(x) = sec x f'(x) = tan^2 x (c) What is ๐ โฒ ( ๐ 4 ) ? [ Select ] 1 2 sqrt(2) 0 4 1/sqrt(2) ย ย
View Explanation
Verified Answer
Please login to view
Step-by-Step Analysis
Letโs break down each part separately and examine the options one by one so the reasoning is clear and reasons for each choice are explicit.
(a) What is f(ฯ/4) for f(x) = tan x?
- Option: 2/sqrt(3) โ 1.15. This would correspond to tan(ฯ/3) or a related angle, but at ฯ/4 the tangent value is not this number.
- Option: 1. This is the actual value of tan(ฯ/4), since tan(ฯ/4) = sin(ฯ/4)/cos(ฯ/4) = (โ2/2)/(โ2/2) = 1.
- Option: -1. This would be the tangent value at an angle in a quadrant where both sine and cosine patterns yield a negative ratio, but ฯ/4 lies in the first quadrant where tan is pos......Login to view full explanationLog in for full answers
We've collected overย 50,000 authentic exam questionsย andย detailed explanationsย from around the globe. Log in now and get instant access to the answers!
Similar Questions
at ็็บฟๆง่ฟไผผๅผไธบ๏ผ ๆ็คบ๏ผat ็็บฟๆง่ฟไผผๅผไธบ๏ผ ใ
The linear approximation of ย ๐ ( ๐ฅ ) = 5 ๐ฅ โ 4 2 ๐ฅ 2 + 1 ย at ย ๐ฅ = โ 3 ย is: Hint: The linear approximation ofย ๐ฆ = ๐ ( ๐ฅ ) ย at ย ๐ฅ = ๐ฅ 0 ย is: ย ย ๐ฟ ( ๐ฅ ) = ๐ โฒ ( ๐ฅ 0 ) ( ๐ฅ โ ๐ฅ 0 ) + ๐ ( ๐ฅ 0 ) .
This is a continuation of the previous question. What is the Linear Approximation ofย ๐ ( ๐ฅ ) = tan โก ๐ฅ ย atย ๐ฅ = ๐ 4 ?
Suppose you want to use a Linear Approximation to approximate 1 25.2 without a calculator.ย Which of the following functions and ๐ฅ -values would be best to use?
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!