मनुष्य के जीवन में शब्दों का महत्व लिखिए
Answers
Answer:
जिस व्यक्ति के जीवन का उद्देश्य और मानसिकता जिस स्तर की होगी, उनकी भाषा के शब्द और उनके मुख्यार्थ भी उसी स्तर के होंगे। समाज में रहकर व्यापार या लोगों से बातचीत के लिए मनुष्य के पास भाषा ही एकमात्र माध्यम है।
Explanation:
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Explanation:
im
x→−6
x+6
10−x
−4
=−
8
1
Step-by-step explanation:
\mapsto{\sf{ }}↦ :So first, we should always try direct substitution:
\bold{↬{ }}↬ :\begin{gathered}\begin{gathered}\lim_{x \to -6}\dfrac{\sqrt{10-x}-4}{x+6} \\\end{gathered}\end{gathered}
x→−6
lim
x+6
10−x
−4
\mapsto{\sf{ }}↦ :Plug -6 in for x:
\begin{gathered}\begin{gathered}\dfrac{\sqrt{10-(-6)}-4}{(-6)+6} \\=\dfrac{\sqrt{16}-4}{-6+6}\\ =\dfrac{4-4}{-6+6}=0/0\end{gathered}\end{gathered}
(−6)+6
10−(−6)
−4
=
−6+6
16
−4
=
−6+6
4−4
=0/0
\rightsquigarrow⇝ :This is the indeterminate form. This doesn't mean the limit does not exist, but rather we need to simplify it first.
\rightsquigarrow⇝ :Looking at the limit, we see that there is a square root in the numerator. Therefore, we can use the difference of two squares to cancel out the square root in the numerator.
\rightsquigarrow⇝ :Recall the difference of two squares formula:
\mapsto{\sf{ }}↦ :\green{(a-b)(a+b)=a^2-b^2}(a−b)(a+b)=a
2
−b
2
\bold{↬{ }}↬ :The expression in the numerator is:
\sqrt{10-x}-4
10−x
−4
\mapsto{\sf{ }}↦ :Therefore, to cancel it out, we need to multiply by:
\sqrt{10-x}+4
10−x
+4
\rightsquigarrow⇝ Essentially, you just change the sign. So, multiply both the numerator and denominator by this expression:
\begin{gathered}\begin{gathered}\lim_{x \to -6}\dfrac{\sqrt{10-x}-4}{x+6}\cdot\dfrac{\sqrt{10-x}+4}{\sqrt{10-x}+4} \\\end{gathered}\end{gathered}
x→−6
lim
x+6
10−x
−4
⋅
10−x
+4
10−x
+4
For the numerator, this is the difference of two squares pattern. Therefore:
\lim_{x \to -6}\dfrac{(\sqrt{10-x})^2-(4)^2}{x+6(\sqrt{10-x}+4)}lim
x→−6
x+6(
10−x
+4)
(
10−x
)
2
−(4)
2
The roots in the numerator cancel. 4 squared is 16.
Simplify:
\lim_{x \to -6}\dfrac{(10-x)-16}{x+6(\sqrt{10-x}+4)}lim
x→−6
x+6(
10−x
+4)
(10−x)−16
Simplify:
\lim_{x \to \ -6}\dfrac{-x-6}{x+6(\sqrt{10-x}+4)}lim
x→ −6
x+6(
10−x
+4)
−x−6
Factor out a negative 1 from the numerator:
\lim_{x \to \ -6}\dfrac{-(x+6)}{(x+6)(\sqrt{10-x}+4)}lim
x→ −6
(x+6)(
10−x
+4)
−(x+6)
The (x+6)s cancel out:
\lim_{x \to \ -6}\dfrac{-1}{(\sqrt{10-x}+4)}lim
x→ −6
(
10−x
+4)
−1
Now, plug -6 again:
\begin{gathered}\begin{gathered}\dfrac{-1}{(\sqrt{10-(-6)}+4)}\\=\dfrac{-1}{\sqrt{16+4}}\\ =\dfrac{-1}{(4+4)}=\dfrac{-1}{8}=-.125\end{gathered}\end{gathered}
(
10−(−6)
+4)
−1
=
16+4
−1
=
(4+4)
−1
=
8
−1
=−.125