Download App

Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives2 Marks
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 & $\mathop {\lim }\limits_{x \to {a_1}} f(x)$? For some $a \ne {a_1},\;{a_2}...{a_n},$ compute $\mathop {\lim }\limits_{x \to {a}} f(x)$
✓

Answer

Here $f(x) = (x – a_1) (x – a_2)… (x – a_n)$
Now $\mathop {\lim }\limits_{x \to {a_1}} f(x) = \mathop {\lim }\limits_{x \to {a_1}} (x - {a_1})(x - {a_2})...(x - {a_n})$
$= (a_1 – a_1) (a_1 – a_2) … (a_1 – a_n)$
$= 0 \times (a_1 – a_2) … (a_1 – a_n) = 0.$
Also $\mathop {\lim }\limits_{x \to a} f(x) = \mathop {\lim }\limits_{x \to a} (x - {a_1})(x - {a_2})...(x - {a_n})$
$= (a – a_1) (a – a_2) … (a – a_n)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Limits and Derivatives→Limits and Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Evaluate $\mathop {\lim }\limits_{x \to \frac{\pi }{2}} \frac{{\tan 2x}}{{x - \frac{\pi }{2}}}$
→
Write the first five terms of the sequence whose $n^{th} $ term is $a_n = n (n + 2)$
→
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
→
Express the following complex numbers in the standard form a + ib:
$\frac{2+3\text{i}}{4+5\text{i}}$
→
What are the odds in favour of getting a spade if a card is drawn from a well $-$ shuffled deck of cards? what are the odds in favour of getting a king?
→
Prove that: $\cos\frac{7\pi}{12}+\cos\frac{\pi}{12}=\sin\frac{5\pi}{12}-\sin\frac{\pi}{12}$
→
If the origin is the centriod of the triangle PQR with vertices P(2a, 2, 6), Q(-4, 3b, -10) and R(8, 14, 2c), then find the values of a, b and c.
→
Find the derivative of function $\frac{{a + b\sin x}}{{c + d\cos x}}$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers)
→
Solve for x, the inequalities Exercises.
$|\text{x}-1|\leq5,\ |\text{x}|\geq2$
→
Solve the inequality $\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}$ for real x.
→