Please answer the question in its entirety. 3.Let function In: (0, ∞0) → R be defined by ln(2) = [dtA. The function In(x) is continuous at every x in its domain. Explain. (Hint: what property does the first fundamental theorem imply about function ln(x).)B. The value of ln(2) is positive and the value of ln(1/2) is negative. Explain.C. Assume the identity In(ab) = ln(a) + ln(b) holds for all positive a, b. Using this identity, we have the following results for any positive integer n:In(2¹) = n. ln(2) and In() = n. ln(). Explain.D. The results of Parts A, B, and C combine to yield that function In(x) has a range of (-∞, ∞). (Hint: Part A implies that the IVT applies, and the IVTworks well with the result from Part C.)

The given function is ln: 0,∞→ℝ be defined by lnx=∫1x1tdt. Given the identity lnab=lna+lnb holds…

3. Let function In: (0, ∞) → R be defined by ln(x) = A. The function In(x) is continuous at every x in its domain. Explain. (Hint: what property does the first fundamental theorem imply about function In(x).) B. The value of In (2) is positive and the value of In(1/2) is negative. Explain. C. Assume the identity In(ab) = ln(a) + In(b) holds for all positive a, b. Using this identity, we have the following results for any positive integer n: In(2¹) = n. ln(2) and ln() = n. ln(). Explain. - dt.

3. Let function In: (0, ∞) → R be defined by ln(x) = A. The function In(x) is continuous at every x in its domain. Explain. (Hint: what property does the first fundamental theorem imply about function In(x).) B. The value of In (2) is positive and the value of In(1/2) is negative. Explain. C. Assume the identity In(ab) = ln(a) + In(b) holds for all positive a, b. Using this identity, we have the following results for any positive integer n: In(2¹) = n. ln(2) and ln() = n. ln(). Explain. - dt.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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