Explanation Given: The calculation lim x → ∞ e − x x 2 = lim x → ∞ − e − x 2 x = lim x → ∞ e − x x = 0 2 = 0 Concept Used: L'Hopital's Rule: If f and g are differentiable functions and g ( x ) is nonzero, and if lim x → c f ( x ) g ( x ) is of the indeterminate form, then lim x → c f ( x ) g ( x ) = lim x → c f ′ ( x ) g ′ ( x ) Calculation: To determine the error in the calculation, lim x → ∞ e − x x 2 = lim x → ∞ − e − x 2 x<

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Concept explainers

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0…

Question

Chapter 3.6, Problem 14C

To determine

To find the error in the calculation,

limx→∞e−xx2=limx→∞−e−x2x=limx→∞e−xx=02=0

And also calculate the limit correctly.

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Chapter 3.6, Problem 13C

Chapter 3.6, Problem 15S

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Chapter 3 Solutions

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To find the error in the calculation, lim x → ∞ e − x x 2 = lim x → ∞ − e − x 2 x = lim x → ∞ e − x x = 0 2 = 0 And also calculate the limit correctly.

Solution Summary: The author explains how to find the error in the calculation and calculate the limit correctly.

Concept explainers

To find the error in the calculation,

limx→∞e−xx2=limx→∞−e−x2x=limx→∞e−xx=02=0

And also calculate the limit correctly.

Want to see the full answer?

Chapter 3 Solutions

To find the error in the calculation, lim x → ∞ e − x x 2 = lim x → ∞ − e − x 2 x = lim x → ∞ e − x x = 0 2 = 0 And also calculate the limit correctly.

Solution Summary: The author explains how to find the error in the calculation and calculate the limit correctly.

Concept explainers

To find the error in the calculation, limx→∞e−xx2=limx→∞−e−x2x=limx→∞e−xx=02=0 And also calculate the limit correctly.

Want to see the full answer?

Chapter 3 Solutions

To find the error in the calculation,

limx→∞e−xx2=limx→∞−e−x2x=limx→∞e−xx=02=0

And also calculate the limit correctly.