Concept explainers
(a) Graph the function
(b) Zoom in to the viewing window [–0.4, 0.4] by [– 0.25, 0.25] and estimate the value of f'(0). Does this agree with your answer from pan (a)?
(c) Now zoom in to the viewing window [– 0.008, 0.008] by [– 0.005, 0.005]. Do you wish to revise your estimate for f'(0)?
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Single Variable Calculus: Early Transcendentals
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus For The Life Sciences
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus and Its Applications (11th Edition)
- A particle travels along the x-axis so that its velocity is given by v(t)= 2 cos t for t >= 0. The position of the particle at t = pi/2 is x=5. The position, x(t), of the particle at any time t is given byarrow_forwardFind the absolute maximum and minimum of f(t) = -2cos2t + sin4t on the interval [0,pi/4]arrow_forward1) The function u(x, t) = 3 sin (2x + t + pi/4) represents a travelling wave with height u at position x and time t. a) what is the waves speed b) when t=0, at what x value does it reach its maximum height in the interval 0 ≤ x ≤ 2pi ? c) when t=pi/4, at what x value does it reach its maximum height in the interval 0 ≤ x ≤ 2pi ? e) when t=0, at what is its maximum height in the interval 0 ≤ x ≤ 2pi ?arrow_forward
- 1. Find all values of x such that the graph of f(x) = x/(1+x^2) has a horizontal tangent line at x. 2. Find the equation of the tangent line to (1+x)/ (1+e^x) at the point (0, 1/2)arrow_forwardFind all values of x in the interval [ -pi/2, pi/2 ]at which the fuction f(x)=sin^2+cos x reaches an absolute minimum value. Note: The only x values in this interval where f'(x)=0 are x= - pi/3 and x= pi/3arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage