Use Leibnitz's Theorem to find the nth derivative of x°ln(x).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve No : 2

2. Use Leibnitz’s Theorem to find the nth derivative of x3ln(x).

dy
1. Given, a"y" = 1. Find
dx
%3D
2. Use Leibnitz's Theorem to find the nth derivative of a ln(x).
3. Find the equation of tangent line of the function f(x) =
8
at the point
(6, 4).
4. Use an appropiate linear approximation to estimate the value of (3.02)ª. Com-
pare your approximation to the result produced directly by a calculating utility.
5. Find the maxima/minima of f(x) = (x – 3)eª using both 1st and 2nd deriva-
tive test.
6. Find the intervals on which f (x) = x³ – x is (a) increasing (b) decreasing (c)
concave up (d) concave down and (e) x-coordinates of all inflection points.
Transcribed Image Text:dy 1. Given, a"y" = 1. Find dx %3D 2. Use Leibnitz's Theorem to find the nth derivative of a ln(x). 3. Find the equation of tangent line of the function f(x) = 8 at the point (6, 4). 4. Use an appropiate linear approximation to estimate the value of (3.02)ª. Com- pare your approximation to the result produced directly by a calculating utility. 5. Find the maxima/minima of f(x) = (x – 3)eª using both 1st and 2nd deriva- tive test. 6. Find the intervals on which f (x) = x³ – x is (a) increasing (b) decreasing (c) concave up (d) concave down and (e) x-coordinates of all inflection points.
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