Calculator limits Use a calculator to make a table similar to Table 7.1 to approximate the following limits. Confirm your result with l’Hôpital’s Rule. Table 7.1(1 + h)'M2.593742 -101 2.867972(1 + h)'hh1010-2 2.704814 -10-2 2.73199910-32.716924 -10-3 2.7196421042.718146 -1042.71841810-5 2.718268 -10-5 2.7182951062.718280 -10-62.71828310-7 2.718282 -107 2.718282 lim (1 + 3h)2/h

Given that limh→01+3h2h. Table the function values of y=1+3x2x as shown below. Thus,…

Table 7.1 (1 + h)'M 2.593742 -101 2.867972 (1 + h)' h h 10 10-2 2.704814 -10-2 2.731999 10-3 2.716924 -10-3 2.719642 104 2.718146 -104 2.718418 10-5 2.718268 -10-5 2.718295 106 2.718280 -10-6 2.718283 10-7 2.718282 -107 2.718282 lim (1 + 3h)2/h

Table 7.1 (1 + h)'M 2.593742 -101 2.867972 (1 + h)' h h 10 10-2 2.704814 -10-2 2.731999 10-3 2.716924 -10-3 2.719642 104 2.718146 -104 2.718418 10-5 2.718268 -10-5 2.718295 106 2.718280 -10-6 2.718283 10-7 2.718282 -107 2.718282 lim (1 + 3h)2/h

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 6E

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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 topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Calculator limits Use a calculator to make a table similar to Table 7.1 to approximate the following limits. Confirm your result with l’Hôpital’s Rule.

Table 7.1
(1 + h)'M
2.593742 -101 2.867972
(1 + h)'
h
h
10
10-2 2.704814 -10-2 2.731999
10-3
2.716924 -10-3 2.719642
104
2.718146 -104
2.718418
10-5 2.718268 -10-5 2.718295
106
2.718280 -10-6
2.718283
10-7 2.718282 -107 2.718282

Expert Solution

Step 1

Given that $\lim_{h \to 0} {(1 + 3 h)}^{\frac{2}{h}}$ .

Table the function values of $y = {(1 + 3 x)}^{\frac{2}{x}}$ as shown below.

Thus, $\lim_{h \to 0} {(1 + 3 h)}^{\frac{2}{h}} \approx 403.428$

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