Let a 1- a 2- - a n be fixed real numbers and define a function f x - x - a 1 x - a 2 - x - a n - What is lim x - a 1 f x -For some a- a 1- a 2- a n- compute lim v f x -

Here f(x) = (x a_1)(x a_2) ...(x a_n) Now x → a_1lim f(x) = x → a_1lim (x a_1)(x a_2) ...(x a_n) = (a_1 a_1) (a_1 a_2)...(a_1 a_n) = 0 × (a a_1) (a a_2) ...(a_1 ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Algebra of Limits

Let a 1, a 2,...

Question

Let $a_{1}$ , $a_{2}$ , ..., $a_{n}$ be fixed real numbers and define a function f(x) = $(x - a_{1}) (x - a_{2}) . . . (x - a_{n})$ . What is $lim x \to a_{1}$ f(x)?
For some a $\neq a_{1}, a_{2} . . . a_{n}$ , compute $lim x \to a$ f(x).

Open in App

Solution

Here f(x) = $(x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

Now $lim x \to a_{1} f (x) = lim x \to a_{1} (x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

= $(a_{1} - a_{1}) (a_{1} - a_{2}) . . . (a_{1} - a_{n})$

= 0 $\times (a - a_{1}) (a - a_{2})$ ... $(a_{1} - a_{n})$ = 0.

Also $lim x \to a f (x) = lim x \to a (x - a_{1}) (x - a_{2}) . . . (x - a_{n})$

= $(a - a_{1}) (a - a_{2}) . . . (a - a_{n})$

Suggest Corrections

Similar questions

Letbe fixed real numbers and define a function

What isf(x)? For some computef(x).

Q. Let

a_{1}, a_{2}, \cdot \cdot \cdot \cdot, a_{n}

be fixed real numbers and define a function

f (x) = (x - a_{1}) (x - a_{2})

.....

(x - a_{n})

What is

lim x \to a_{1} f (x) ?

For some

a \neq a_{1}, a_{2} \cdot \cdot \cdot, a_{n},

compute

lim x \to a f (x) \cdot

Q. Let

a_{1}, a_{2}, . . ., a_{n}

be fixed real numbers and define a function

f (x) = (x - a_{1}) (x - a_{2}) . . . . (x - a_{n})

.
What is

lim x \to a_{1} f (x)

? For some

a \neq a_{1}, a_{2}, . . ., a_{n}

, compute

lim x \to a f (x)

Let $a_{1}, a_{2}, \dots, a_{n}$ be fixed real numbers and define a function $f (x) = (x - a_{1}) (x - a_{2}) \dots (x - a_{n})$
What is $lim x \to a_{1} f (x) ?$ For some $a \neq a_{1}, a_{2} \dots . a_{n}$ compute $lim x \to a f (x)$ .

Let $a_{1}, a_{2}, . . . . ., a_{n}$ be fixed real numbers such that $f (x) = (x - a_{1}) (x - a_{2}) . . . . (x - a_{n})$ What is $l i m_{x \to a_{1}}$ f(x)? For $a \neq a_{1}, a_{2}, . . . ., a_{n}$ compute $l i m_{x \to a} f (x) .$

Join BYJU'S Learning Program

Let a1, a2, ..., an be fixed real numbers and define a function f(x) = (x−a1)(x−a2)...(x−an). What is limx→a1 f(x)? For some a ≠a1,a2...an, compute limx→a f(x).

Here f(x) = (x−a1)(x−a2)...(x−an) Now limx→a1f(x)=limx→a1(x−a1)(x−a2)...(x−an) = (a1−a1)(a1−a2)...(a1−an) = 0 ×(a−a1)(a−a2) ...(a1−an) = 0. Also limx→af(x)=limx→a(x−a1)(x−a2)...(x−an) = (a−a1)(a−a2)...(a−an)

Let $a_{1}$ , $a_{2}$ , ..., $a_{n}$ be fixed real numbers and define a function f(x) = $(x - a_{1}) (x - a_{2}) . . . (x - a_{n})$ . What is $lim x \to a_{1}$ f(x)?
For some a $\neq a_{1}, a_{2} . . . a_{n}$ , compute $lim x \to a$ f(x).