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. The table below gives the values of distance traveled by a car at various times from a tollgate at highway. Time, t (minute) Distance traveled, x (km) 3 5 7 9 11 4.6 8.030 11.966 16.885 19.904 Given that velocity, v=x'(t). By taking h=2 minutes, estimate the velocity at time t= 5 minutes by appropriate difference formulas given in Table 5.1.

. The table below gives the values of distance traveled by a car at various times from a tollgate at highway. Time, t (minute) Distance traveled, x (km) 3 5 7 9 11 4.6 8.030 11.966 16.885 19.904 Given that velocity, v=x'(t). By taking h=2 minutes, estimate the velocity at time t= 5 minutes by appropriate difference formulas given in Table 5.1.

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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SUMMARY 5 Table 5.1: The Difference Formula Truncation Error O(h) First derivative, 2-point forward difference S(t) L+h)-/(x) O(h) 2-point backward f(x)- f(x-h) difference 3-point central difference 3-point forward difference f(x+h)-f(x-h) f(x) = 2h -3/(x)+4f(x+h)-f(x+2h) f'(x)= 2h ()= (x-2h)-4/(x-h)+3f(x) 2h 3-point backward difference 5-point central difference Second derivatives, 3-point central difference f(x) = f(x-2h)-8f(x-h) + 8ƒ(x+h)-ƒ(x+2h) 12h f'(x) f"(x) = f(x-h)-2/(x)+ f(x+h) O() 5-point central difference -f(x-2h) + 16f(x - h)-30/(x) +16/(x+h)-f(x+2h) 121
Transcribed Image Text:SUMMARY 5 Table 5.1: The Difference Formula Truncation Error O(h) First derivative, 2-point forward difference S(t) L+h)-/(x) O(h) 2-point backward f(x)- f(x-h) difference 3-point central difference 3-point forward difference f(x+h)-f(x-h) f(x) = 2h -3/(x)+4f(x+h)-f(x+2h) f'(x)= 2h ()= (x-2h)-4/(x-h)+3f(x) 2h 3-point backward difference 5-point central difference Second derivatives, 3-point central difference f(x) = f(x-2h)-8f(x-h) + 8ƒ(x+h)-ƒ(x+2h) 12h f'(x) f"(x) = f(x-h)-2/(x)+ f(x+h) O() 5-point central difference -f(x-2h) + 16f(x - h)-30/(x) +16/(x+h)-f(x+2h) 121
8. The table below gives the values of distance traveled by a car at various times from a tollgate at highway. 9 11 Time, t (minute) Distance traveled, x (km) 3 5 7 4.6 8.030 11.966 16.885 19.904 Given that velocity, v=x'(t). By taking h=2 minutes, estimate the velocity at time t = 5 minutes by appropriate difference formulas given in Table 5.1.
Transcribed Image Text:8. The table below gives the values of distance traveled by a car at various times from a tollgate at highway. 9 11 Time, t (minute) Distance traveled, x (km) 3 5 7 4.6 8.030 11.966 16.885 19.904 Given that velocity, v=x'(t). By taking h=2 minutes, estimate the velocity at time t = 5 minutes by appropriate difference formulas given in Table 5.1.
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