Plz fast Q Example 88 Let f (x) be a periodic function with period 3 and f - Maths - Relations and Functions

Question

Plz fast

Q Example 88 Let f (x) be a periodic
function with period 3 and f - 2 3 = 7   and   g ( x
)   = ∫ 0 x t   + n   dt ,   where   n
  = 3 K ,   K ∈ N Then g' 7 3 is equal to

(a) - 2 3 (b) 7

(c) – 7 (d) 7 3

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

f-23=7We have period of fx as 3
Hence period of fx will also be all other multiples of 3, Nowgx=∫0xft+n dtNow as n=3K, K∈NAs n is multiple of 3, hence it will also be period of function 'f'
Hence ft+n=ft⇒gx=∫0xft dtDifferentiate both sides with respect to x using Lebnitz ruleg'x=fx
ddxx-f0ddx0⇒g'x=fx×1-0⇒g'x=fxPut x=-23⇒g'-23=f-23⇒g'-23=7

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Plz fast Q. Example 88. Let f (x) be a periodic function with period 3 and f - 2 3 = 7 and g ( x ) = ∫ 0 x t + n dt , where n = 3 K , K ∈ N . Then g' 7 3 is equal to (a) - 2 3 (b) 7 (c) – 7 (d) 7 3

Plz fast

Q. Example 88. Let f (x) be a periodic function with period 3 and f $(- \frac{2}{3}) = 7 and g (x)$ $= \int_{0}^{x} (t + n) dt, where n = 3 K, K \in N$ . Then g' $(\frac{7}{3})$ is equal to

(a) $- \frac{2}{3}$ (b) 7

(c) – 7 (d) $\frac{7}{3}$