Explanation Given: The function is lim x → π 2 ( x − π 2 ) tan x . Formula used: The limit law is lim x → c x = c . The product law: If lim x → c f ( x ) and lim x → c g ( x ) both exists, then lim x → c ( f ( x ) g ( x ) ) = ( lim x → c f ( x ) ) ( lim x → c g ( x ) ) Calculation: We have to show that the product rule is not applicable for the function lim x → π 2 ( x − π 2 ) tan x

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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…

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Chapter 2.3, Problem 32E

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Check the product law is not applicable to evaluate limx→π2(x−π2)tanx. Give reason.

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Chapter 2.3, Problem 31E

Chapter 2.3, Problem 33E

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Draw the following solid and explain each step to obtain the final result of the volume (see image):

A cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is 20°C and the temperature of the cake when it was taken out of the oven is 160°C (a) Given that the temperature of the cake is governed by Newton's law of cooling, write down a differential equation governing T(t), the temperature of the cake after t hours. What is the appropriate initial condition? (Newton's law of cooling: dT dt =-K(T-Ta), where K is a constant and Ta is the ambient temperature.) (b) From you answer in part (a), derive the solution T(t) = 20 + 140e Kt, where K is a (c) constant. Given that the cake has cooled to 90°C after 1 hour, determine the constant K. (d) The cook decides that the cake is cool enough to be taken out of the cake pan when its temperature lowers to 40 degrees C. Find when this will happen, both in exact form and as a decimal approximation to at least 2 decimal places, showing all working.

Chapter 2 Solutions

Calculus - Standalone book

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 5PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E

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Check the product law is not applicable to evaluate lim x → π 2 ( x − π 2 ) tan x . Give reason.

Solution Summary: The author explains that the product law is not applicable because undersetxto 0mathrmlim

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Check the product law is not applicable to evaluate limx→π2(x−π2)tanx. Give reason.

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Chapter 2 Solutions