The audible range of frequency is (a) 200 Hz - 2000 Hz (b) 20 Hz - 2000 Hz (c) 20 Hz - 35,000 (d) 220 Hz - 20,000 Hz
Answers
Answer:
about 20 Hz to 20 kHz
Explanation:
Humans can detect sounds in a frequency range from about 20 Hz to 20 kHz. (Human infants can actually hear frequencies slightly higher than 20 kHz, but lose some high-frequency sensitivity as they mature; the upper limit in average adults is often closer to 15–17 kHz.)
Answer:
Answer:
sinα - αcosα
Step-by-step explanation:
Given that,
\lim_{x\to\alpha}\;\;|\frac{x\sin\alpha-\alpha\sin x}{x-\alpha}|lim
x→α
∣
x−α
xsinα−αsinx
∣
Let x - α = h
Thus when x ⇒ α , h ⇒ 0
\lim_{h\to0}\;\;|\frac{(h+\alpha)\sin\alpha-\alpha\sin(h+\alpha)}{h}|lim
h→0
∣
h
(h+α)sinα−αsin(h+α)
∣
Now we will evaluate left hand limit and right and limit separately
For LHL:-
\begin{gathered}\begin{gathered}\lim_{h\to0}\;\;\frac{\alpha\sin\alpha[1-\cos(-h)]}{-h}+\sin\alpha-\frac{\alpha\sin(-h)\cos\alpha}{-h}\\\;\\=\lim_{h\to0}\;\;\frac{\alpha\sin\alpha(1-\cosh)}{-h}+\sin\alpha-\frac{\alpha\sin h\cos\alpha}{h}\\\;\\=\alpha\sin\alpha[\lim_{h\to0}\frac{(1-\cosh)}{-h}]+\sin\alpha-\alpha\cos \alpha[\lim_{h\to0}\frac{\sin h}{h}]\\\;\\=0+\sin\alpha-\alpha\cos\alpha\\\;\\=\sin\alpha-\alpha\cos\alpha\end{gathered} \end{gathered}
h→0
lim
−h
αsinα[1−cos(−h)]
+sinα−
−h
αsin(−h)cosα
=
h→0
lim
−h
αsinα(1−cosh)
+sinα−
h
αsinhcosα
=αsinα[
h→0
lim
−h
(1−cosh)
]+sinα−αcosα[
h→0
lim
h
sinh
]
=0+sinα−αcosα
=sinα−αcosα
For RHL:-
\begin{gathered}\begin{gathered}\lim_{h\to0}\;\;\frac{\alpha\sin\alpha[1-\cosh]}{h}+\sin\alpha-\frac{\alpha\sinh\cos\alpha}{h}\\\;\\=\lim_{h\to0}\;\;\frac{\alpha\sin\alpha(1-\cosh)}{h}+\sin\alpha-\frac{\alpha\sin h\cos\alpha}{h}\\\;\\=\alpha\sin\alpha[\lim_{h\to0}\frac{(1-\cosh)}{h}]+\sin\alpha-\alpha\cos \alpha[\lim_{h\to0}\frac{\sin h}{h}]\\\;\\=0+\sin\alpha-\alpha\cos\alpha\\\;\\=\sin\alpha-\alpha\cos\alpha\end{gathered} \end{gathered}
h→0
lim
h
αsinα[1−cosh]
+sinα−
h
αsinhcosα
=
h→0
lim
h
αsinα(1−cosh)
+sinα−
h
αsinhcosα
=αsinα[
h→0
lim
h
(1−cosh)
]+sinα−αcosα[
h→0
lim
h
sinh
]
=0+sinα−αcosα
=sinα−αcosα
Thus limit is (sinα - αcosα).