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**Question 1: The solution at x = 1, t = 1 of the partial differential equation subject to initial conditions of u(0) ______.****(a) 1 (b) 2(c) 4(d) 6**

Dâ€™Alembertâ€™s formula,

u(x, t) = 3x + 3t

At x = 1, t = 1

u(x, f) = 6

**f(x) = 0, (-Ï€ < x < 0 )**

** f(x) = ****Ï€**** - x,**** (0 < x < Ï€) in the interval [- Ï€, Ï€] is****The convergence of the above Fourier series at x = 0 gives**** [2016 : 1 Mark, Set-II]****Answer: (c)****Solution: **The function is f(x) = 0,

-p < x __<__ 0

= p - x, 0 < x < Ï€

And Fourier series is,

At x = 0, (a point of discontinuity), the fourier series

Hence, eq. (i), we get,

â‡’ **Question 3: The infinite series corresponds to(a) secx(b) e**

(By McLaurinâ€™s series expansion)

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