1. Find particular solution of the following differential equation: dy 15- + 2r-3 dr - 3x-2 =0 Boundary condition: y=0 when x-1

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Find particular solution of the following differential equation:
dy
15 –
+ 2r
3x
= 0
dr
Boundary condition: y=0 when x=1
2. Using m-6 steps, estimate the value of the definite integral
(2.x+x+1)dx
r=1
(a) Using the Simpson's rule
(b) Calculate the exact value of the integral by analytical means.
3. Find:
(a) f"(x)wheref(x) = e4# – e-4z
(b) fliv) (x)wheref (x) =
100
e-0.5z
1/µ
(c) " ue-utdt
4. What is the doubling time for:
(a) a population growing at 3.5% per annum;
(b) a debt on which interest is charged at 36% p.a.
5. Maximize
z = 2.x2+ 6xy + 100r
subject to x+y=5. Use sufficient second-order condition to confirm the maximum.
Transcribed Image Text:1. Find particular solution of the following differential equation: dy 15 – + 2r 3x = 0 dr Boundary condition: y=0 when x=1 2. Using m-6 steps, estimate the value of the definite integral (2.x+x+1)dx r=1 (a) Using the Simpson's rule (b) Calculate the exact value of the integral by analytical means. 3. Find: (a) f"(x)wheref(x) = e4# – e-4z (b) fliv) (x)wheref (x) = 100 e-0.5z 1/µ (c) " ue-utdt 4. What is the doubling time for: (a) a population growing at 3.5% per annum; (b) a debt on which interest is charged at 36% p.a. 5. Maximize z = 2.x2+ 6xy + 100r subject to x+y=5. Use sufficient second-order condition to confirm the maximum.
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