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DB_2023
HSC - উচ্চতর গণিত ১ম পত্র
→
অধ্যায়-১০ঃ যোগজীকরণ
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f
(
x
)
=
ln
(
2
x
)
\mathrm {f(x)=\ln (2 x)}
f
(
x
)
=
ln
(
2x
)
হলে —
i.
f
′
(
x
)
=
1
x
ii.
∫
f
(
x
)
d
x
=
x
(
ln
∣
2
x
∣
−
1
)
+
c
iii.
∫
1
1
2
f
(
x
)
d
x
=
1
2
−
ln
2
\begin{array}{l}\text{i. } \quad ~~ \mathrm {f^{\prime}(x)=\dfrac{1}{x}}\\\text{ii. } \quad ~ \mathrm {\int f(x) d x=x(\ln |2 x|-1)+c}\\\text{iii. } \quad \mathrm {\int_{1}^{\frac{1}{2}} \mathrm{f}(\mathrm{x}) \mathrm{dx}=\dfrac{1}{2}-\ln 2}\end{array}
i.
f
′
(
x
)
=
x
1
ii.
∫
f
(
x
)
dx
=
x
(
ln
∣2x∣
−
1
)
+
c
iii.
∫
1
2
1
f
(
x
)
dx
=
2
1
−
ln
2
নিচের কোনটি সঠিক ?
A.
i ও ii
B.
i ও iii
C.
ii ও iii
D.
i, ii ও iii
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