Let a1, a2, a3, ldots ldots ldots, an be fixed real numbers and define a function f(x)=(x-a1)(x-a2) ldots ldots(x-an), then

Question

Let a1, a2, a3, ldots ldots ldots, an be fixed real numbers and define a function f(x)=(x-a1)(x-a2) ldots ldots(x-an), then (A)  displaystyle lim x arrow a1 f(x)=0 (B)  displaystyle lim x arrow a f(x)=(a-a1)(a-a2) ldots ldots . .(a-an), for some a ≠ a1, (C) Both (a) and (b) are true (D) Either (a) or (b) is true

Tardigrade Admin · Accepted Answer

Given, f(x)=(x-a1)(x-a2) ldots .(x-an) ∴ displaystyle lim x arrow a1 f(x) = displaystyle lim x arrow a1(x-a1)(x-a2) ldots(x-an) =(a1-a1)(a1-a2) ldots .(a1-an) =0 ×(a1-a2) ldots(a1-an)=0 Again, displaystyle lim x arrow a f(x)= displaystyle lim x arrow a(x-a1)(x-a2) ldots(x-an) =(a-a1)(a-a2) ldots(a-an)

Q. Let $a_{1}, a_{2}, a_{3}, \dots\dots\dots, a_{n}$ be fixed real numbers and define a function $f (x) = (x - a_{1}) (x - a_{2}) \dots\dots (x - a_{n})$ , then

$x \to a_{1} lim f (x) = 0$

$x \to a lim f (x) = (a - a_{1}) (a - a_{2}) \dots\dots .. (a - a_{n})$ , for some $a \neq = a_{1}$ ,

Both (a) and (b) are true

Either (a) or (b) is true

Q. Let a1​,a2​,a3​,………,an​ be fixed real numbers and define a function f(x)=(x−a1​)(x−a2​)……(x−an​), then

x→a1​lim​f(x)=0

x→alim​f(x)=(a−a1​)(a−a2​)……..(a−an​), for some a=a1​,

Both (a) and (b) are true

Either (a) or (b) is true

Q. Let $a_{1}, a_{2}, a_{3}, \dots\dots\dots, a_{n}$ be fixed real numbers and define a function $f (x) = (x - a_{1}) (x - a_{2}) \dots\dots (x - a_{n})$ , then

$x \to a_{1} lim f (x) = 0$

$x \to a lim f (x) = (a - a_{1}) (a - a_{2}) \dots\dots .. (a - a_{n})$ , for some $a \neq = a_{1}$ ,