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Q7,11,15 &Q17 needed These are easy questions Kindly solve all in the order to get positive feedback Please do all otherwise don't solve Neat and clean work needed

Q7,11,15 &Q17 needed These are easy questions Kindly solve all in the order to get positive feedback Please do all otherwise don't solve Neat and clean work needed

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q7,11,15 &Q17 needed These are easy questions Kindly solve all in the order to get positive feedback Please do all otherwise don't solve Neat and clean work needed
EXERCISES 4.5 Differentiate the following functions. 1. y 3 ln x + In 2 x² In x 2 5. ye ln x In x Vx 9. y = ln x² 3. y= 7. y= In (=) 13. yIn(3x4x²) 1 In x 11. y In( 15. y = 17. y = In x In 2x 19. y (x³ + 1) In(x³ + 1) Find the second derivatives. d² 21. (1² In 1) dr² 2. y = 4. y 8. y= In x In 3 3 X 6. y = el +Inx In x 20. y = 1 2 + 3 ln x 10. y = In √x In(-1/2) ln(e +ex) 12. y In 14. y 16. y In x ln 2x 18. y = (In x)2 In(x² + 1) x²+1 d² 22.2ln(In 1) 23. The graph of f(x) = (In x)/√x is shown in Fig. 4. Find the coordinates of the maximum point. 1 4 Y 25 Figure 4 24. The graph of f(x) = x/(lnx + x) is shown in Fig. 5. Find the coordinates of the minimum point. x 10 Figure 5 25. Write the equation of the tangent line to the graph of ln(x² + e) at x = 0. y 26. The function f(x) = (In x + 1)/x has a relative extreme point for x > 0. Find the coordinates of the point. Is it a relative maximum point?
Transcribed Image Text:EXERCISES 4.5 Differentiate the following functions. 1. y 3 ln x + In 2 x² In x 2 5. ye ln x In x Vx 9. y = ln x² 3. y= 7. y= In (=) 13. yIn(3x4x²) 1 In x 11. y In( 15. y = 17. y = In x In 2x 19. y (x³ + 1) In(x³ + 1) Find the second derivatives. d² 21. (1² In 1) dr² 2. y = 4. y 8. y= In x In 3 3 X 6. y = el +Inx In x 20. y = 1 2 + 3 ln x 10. y = In √x In(-1/2) ln(e +ex) 12. y In 14. y 16. y In x ln 2x 18. y = (In x)2 In(x² + 1) x²+1 d² 22.2ln(In 1) 23. The graph of f(x) = (In x)/√x is shown in Fig. 4. Find the coordinates of the maximum point. 1 4 Y 25 Figure 4 24. The graph of f(x) = x/(lnx + x) is shown in Fig. 5. Find the coordinates of the minimum point. x 10 Figure 5 25. Write the equation of the tangent line to the graph of ln(x² + e) at x = 0. y 26. The function f(x) = (In x + 1)/x has a relative extreme point for x > 0. Find the coordinates of the point. Is it a relative maximum point?
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