where [.⋅ ]. is the greatest integer function. If f is a continuous function, then ab=(√λ /μ ) . Find value of λ μ (where λ ,μ are coprime to each other)

Question

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6edaa4e32ea8c0be2dc4d6af92e69d3b-.png" /> where [.⋅ ]. is the greatest integer function. If f is a continuous function, then ab=(√λ /μ ) . Find value of λ μ (where λ ,μ are coprime to each other) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(x)= beginarrayll(a+3 cos x/x2), x<0 b tan ((π/[x+3])), x ≥ 0 endarray. f(0-)=(-3/2), a=-3 f(0+)=√3 b, b=(-√3/2)

Q. where $[\cdot]$ is the greatest integer function. If $f$ is a continuous function, then $ab = \frac{λ}{μ}$ . Find value of $λ μ$ (where $λ, μ$ are coprime to each other)

$f (x) = {\frac{a + 3 c o s x}{x ^{2}}, b tan (\frac{π}{[ x + 3 ]}), x \geq 0 x < 0$
$f (0^{-}) = \frac{- 3}{2}, a = - 3$
$f (0^{+}) = 3 b, b = \frac{- 3}{2}$

Q. where [⋅] is the greatest integer function. If f is a continuous function, then ab=μλ​​ . Find value of λμ (where λ,μ are coprime to each other)

f(x)={x2a+3cosx​,btan([x+3]π​),x≥0​x<0 f(0−)=2−3​,a=−3 f(0+)=3​b,b=2−3​​

Q. where $[\cdot]$ is the greatest integer function. If $f$ is a continuous function, then $ab = \frac{λ}{μ}$ . Find value of $λ μ$ (where $λ, μ$ are coprime to each other)

$f (x) = {\frac{a + 3 c o s x}{x ^{2}}, b tan (\frac{π}{[ x + 3 ]}), x \geq 0 x < 0$
$f (0^{-}) = \frac{- 3}{2}, a = - 3$
$f (0^{+}) = 3 b, b = \frac{- 3}{2}$