Explanation Given Information: The provided limit notation is lim x → 0 2 x 2 + x sin x . Formula used: By the trigonometric property, sin ( − θ ) = − sin ( θ ) Calculation: Consider the provided limit notation, lim x → 0 2 x 2 + x sin x . In making the table, choose the value of x close to 0 from the left and from the right as x approaches 0. As x approaches 0 from the left arbitrarily start with x = − 0.01 . Then select two additional values of x that are closer to 0, but still less than 0, we choose − 0.001 and − 0.0001 . Evaluate f at each chosen value of x to obtain the corresponding values of f ( x ) . All the values of x are in radian. At x = − 0.01 , Substitute, x = − 0.01 in the provided limit notation, lim x → 0 2 x 2 + x sin x . Therefore, lim x → − 0.01 2 x 2 + x sin x = 2 ( − 0.01 ) 2 + ( − 0.01 ) sin ( − 0.01 ) Apply the trigonometric property, sin ( − θ ) = − sin ( θ ) lim x → − 0.01 2 x 2 + x sin x = 2 ( 0.0001 ) − 0.01 − sin ( 0.01 ) = 0.0002 − 0.01 − 0.0099 = − 9.8 × 10 − 3 − 0.0099 = 0.9800 Now, at x = − 0.001 Substitute, x = − 0.001 in the provided limit notation, lim x → 0 2 x 2 + x sin x . lim x → − 0.001 2 x 2 + x sin x = 2 ( − 0.001 ) 2 + ( − 0.001 ) sin ( − 0.001 ) Apply the trigonometric property, sin ( − θ ) = − sin ( θ ) Therefore, lim x → − 0.001 2 x 2 + x sin x = 2 ( 1 × 10 − 6 ) − 0.001 − sin ( 0.001 ) = ( 2 × 10 − 6 ) − 0.001 − ( 9.99 × 10 − 4 ) = − 9.98 × 10 − 4 − ( 9.99 × 10 − 4 ) = 0.9980 At x = − 0.0001 Substitute, x = − 0.0001 in the provided limit notation, lim x → 0 2 x 2 + x sin x . lim x → − 0.0001 2 x 2 + x sin x = 2 ( 0.0001 ) 2 + ( − 0.0001 ) sin ( − 0.0001 ) Apply the trigonometric property, sin ( − θ ) = − sin ( θ ) lim x → − 0.0001 2 x 2 + x sin x = 2 ( 1 × 10 − 8 ) − 0.0001 − sin ( 0.0001 ) = ( 2 × 10 − 8 ) − 0

6th Edition

ISBN: 9780135963173

Author: Blitzer

Publisher: PEARSON CO

See similar textbooks

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

Videos

Question

Chapter 11.1, Problem 13PE

To determine

To calculate: The value of limit, limx→02x2+xsinx by constructing a table for different values of x.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 12PE

Chapter 11.1, Problem 14PE

Students have asked these similar questions

This question is a previous exam question. I am using it for practice but am stuck

in Q. A firm price of 501: If the Total cast is given by perfect competition sells its products at the TTC = 3Q² +2Q+5. level of output will will be the level of profit at What What Devive the Consumer Curve approach. demand the function maximize this firm's, that using putput level. the indifference prpfit. Q₂. The Total Cost equation in the production of bacon has hypothetical factor a 2 A C= "TC 1000+ 159" +03 ; Where ç. Kash, Bacao - metric bone Compute and 11" tonnes the and average cost at output level of 10. Stretch theme marginal cost of the the shope Carve an the production average, Cost arve 12 tonnes and explain, the relationship between Marginal Cost product es tamen op d Galaxy A71 01 Curve in

if w(x, y, z) = sin' ( xyz) (y zî + x z j + xy k) Find grad (div) at (0.5, 1, 0.5) (xyz)2

Chapter 11 Solutions

EP PRECALCULUS-MYLABMATH+ETEXT ACCESS

Ch. 11.1 - Check Point 1 Find: . Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 5CP Ch. 11.1 - Prob. 1CVC Ch. 11.1 - Prob. 2CVC Ch. 11.1 - Prob. 3CVC Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...

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 value of limit, lim x → 0 2 x 2 + x sin x by constructing a table for different values of x .

Solution Summary: The author calculates the value of the provided limit notation by constructing a table for different values of x.

Concept explainers

Videos

To calculate: The value of limit, limx→02x2+xsinx by constructing a table for different values of x.

Want to see the full answer?

Chapter 11 Solutions