Explanation Given: f ( x ) = x 2 sin x c = π 3 Formula Used: i. The derivative of y = f ( x ) at c is given by: f ′ ( c ) = lim x → c f ( x ) − f ( c ) x − c ii. For any two functions f ( x ) and g ( x ) we have: d d x [ f ( x ) g ( x ) ] = f ′ ( x ) g ( x ) + f ( x ) g ′ ( x ) Calculation: Here, f ( x ) = x 2 sin x ...

11th Edition

ISBN: 9780135228982

Author: Sullivan

Publisher: PEARSON

See similar textbooks

Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Videos

Question

Chapter 14.4, Problem 39AYU

To determine

To find: The derivative of $f (x) = x^{2} \sin x$ at $\frac{π}{3}$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 38AYU

Chapter 14.4, Problem 40AYU

Students have asked these similar questions

2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the mixture is allowed to flow out of the tank at a rate of 3 gal/min. a. Find the amount of salt in the tank at any time prior to the instant when the tank begins to overflow (650 gallons). b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits 400 gallons. D.E. for mixture problems: dv dt=11-12 dA A(t) dt

- Suppose that you have the differential equation: dy = (y - 2) (y+3) dx a. What are the equilibrium solutions for the differential equation? b. Where is the differential equation increasing or decreasing? Show how you know. Showing them on the drawing is not enough. c. Where are the changes in concavity for the differential equation? Show how you know. Showing them on the drawing is not enough. d. Consider the slope field for the differential equation. Draw solution curves given the following initial conditions: i. y(0) = -5 ii. y(0) = -1 iii. y(0) = 2

5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I purposefully removed the units- don't worry about them. Assume no conversions are needed.) a) Find the equation for the displacement of the spring mass at time t. b) Write the equation for the displacement of the spring mass in phase-mode form. c) Characterize the damping of the spring mass system as overdamped, underdamped or critically damped. Explain how you know. D.E. for Spring Mass Systems k m* g = kLo y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo m 2 A₁ = √c₁² + C₂² Q = tan-1

Chapter 14 Solutions

EBK PRECALCULUS

Ch. 14.1 - Graph f( x )={ 3x2ifx2 3ifx=2 (pp.100-102)Ch. 14.1 - Prob. 2AYU Ch. 14.1 - Prob. 3AYU Ch. 14.1 - Prob. 4AYU Ch. 14.1 - True or False lim xc f( x )=N may be described by...Ch. 14.1 - Prob. 6AYU Ch. 14.1 - lim x2 ( 4 x 3 )Ch. 14.1 - lim x3 ( 2 x 2 +1 )Ch. 14.1 - lim x0 x+1 x 2 +1 Ch. 14.1 - Prob. 10AYU

Additional Math Textbook Solutions

Find more solutions based on key concepts

the surface area.

Pre-Algebra Student Edition

CLT Shapes (Example 4) One of the histograms is a histogram of a sample (from a population with a skewed distri...

Introductory Statistics

76. Dew Point and Altitude The dew point decreases as altitude increases. If the dew point on the ground is 80°...

College Algebra with Modeling & Visualization (5th Edition)

Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5. What is the probability t...

A First Course in Probability (10th Edition)

Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis t...

Elementary Statistics: Picturing the World (7th Edition)

CHECK POINT I You deposit $1000 in a saving account at a bank that has a rate of 4%. a. Find the amount, A, of ...

Thinking Mathematically (6th Edition)

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The derivative of f ( x ) = x 2 sin x at π 3 .

Solution Summary: The author explains how the derivative of f (x) = x 2 sin 3 is given by the graphing utility calculator.

Concept explainers

Videos

To find: The derivative of $f (x) = x^{2} \sin x$ at $\frac{π}{3}$ .

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

The derivative of f ( x ) = x 2 sin x at π 3 .

Solution Summary: The author explains how the derivative of f (x) = x 2 sin 3 is given by the graphing utility calculator.

Concept explainers

Videos

To find: The derivative of f( x ) = x 2 sinx at π 3 .

Want to see the full answer?

Chapter 14 Solutions

Additional Math Textbook Solutions

To find: The derivative of $f (x) = x^{2} \sin x$ at $\frac{π}{3}$ .