Download App

Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits3 Marks
Question
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 $\lim\limits_{\text{x}\rightarrow\text{a}_1}\text{f(x)}?$ For $\text{a}\ne\text{a}_1,\text{a}_2,\dots\text{a}_\text{n}$ compute $\lim\limits_{\text{x}\rightarrow{\text{a}}}\text{f(x)}.$
✓

Answer

$\lim\limits_{\text{x}\rightarrow{\text{a}}}\text{f(x)}$
$\Rightarrow\lim\limits_{\text{x}\rightarrow\text{a}_1}({\text{x}-{\text{a}_1}})(\text{x}-\text{a}_2)\dots(\text{x}-\text{a}_\text{n})$ [Putting limits $x \rightarrow a_1$]
$\Rightarrow(\text{a}_1-\text{a}_1)(\text{a}_1-\text{a}_2)\dots(\text{a}_1-\text{a}_\text{n})$
$\Rightarrow0$
And,
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\text{f(x)}$
$\Rightarrow\lim\limits_{\text{x}\rightarrow{\text{a}}}(\text{x}-\text{a}_1)(\text{x}-\text{a}_2)\dots(\text{x}-\text{a}_\text{n})$ [Putting limit $x \rightarrow a$]
$\Rightarrow(\text{a}-\text{a}_1)(\text{a}-\text{a}_2)\dots(\text{a}-\text{a}_\text{n}).$

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 "Solve the Following Question.(3 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the modulus and argument of the following complex numbers and hence express each of them in the polar form:
$\frac{1-\text{i}}{1+\text{i}}$
→
How many $3$-digit even number can be made using the digits $1, 2, 3, 4, 5, 6, 7,$ if no digits is repeated?
→
Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5 , 10, 15, 20}. Find:
  1. A - B
  2. A - C
  3. A - D
  4. B - A
  5. C - A
  6. D - A
  7. B - C
  8. B - D.
→
Let R be a relation on N × N defined by:
$(\text{a, b})\text{ R }(\text{c, d})\Leftrightarrow\text{a}+\text{d}=\text{b}+\text{c}$ for all $(\text{a, b}),(\text{c, d})\in\text{N}\times\text{N}$
Show that:
$(\text{a},\text{b})\text{ R }(\text{c, d})\text{ and (c, d) R (e, f)}$
$\Rightarrow(\text{a, b})\text{ R (e, f)}$ for all $(\text{a, b}),(\text{c, d}),(\text{e, f})\in\text{N}\times\text{N}$
→
The length L (in centimeters) of a copper rod is a linear function of its celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.
→
Find the equation of the straight line upon which the length of the perpendicular from the origin is 2 and the slope of this perpendicular is $\frac{5}{12}.$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\tan\text{x}}{1-\cos\text{x}}$
→
A(5, 3), B(3, -2) are two fixed points; find the equation to the locus of a point P which moves so that the area of the triangle PAB is 9 units.
→
Find the degree and radian measures of exterior and interior angles of a regular : pentagon
→
If A.M. and G.M. of two positive numbers a and b are 10 and 8 respectively, find the numbers.
→