Evaluation of Limits MCQ Quiz in বাংলা - Objective Question with Answer for Evaluation of Limits - বিনামূল্যে ডাউনলোড করুন [PDF]
Last updated on Mar 9, 2025
Latest Evaluation of Limits MCQ Objective Questions
Evaluation of Limits Question 1:
\(\lim_{x\rightarrow 0} \frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\) এর মান কত?
Answer (Detailed Solution Below)
Evaluation of Limits Question 1 Detailed Solution
গণনা
\(\lim \limits_{x\rightarrow 0} \dfrac{1-\cos 2x}{x(\tan 4x)}(3+\cos x)\)
⇒ \(\lim \limits_{x\rightarrow 0} 2\left(\dfrac{\sin x}{x}\right)^{2}.\dfrac{1}{4}\left(\dfrac{4x}{\tan 4x }\right)(3+\cos x)\)
⇒ \(2\times 1\times\dfrac{1}{4}\times 1\times(3+1)=2\)
অতএব, বিকল্প 3 সঠিক।
Evaluation of Limits Question 2:
\(\rm \lim_{n\rightarrow \infty}\left[\left(\frac{1}{2.3}+\frac{1}{2^2.3}\right)+\left(\frac{1}{2^2.3^2}+\frac{1}{2^3.3^2}\right)+....+\left(\frac{1}{2^n.3^n}+\frac{1}{2^{n+1}.3^n}\right)\right]\) এর মান
Answer (Detailed Solution Below)
Evaluation of Limits Question 2 Detailed Solution
Evaluation of Limits Question 3:
f(x) একটি অবকলন যোগ্য অপেক্ষক এবং f' (2) = 6, f(1) = 4 দেওয়া আছে।
সেক্ষেত্রে, \(\rm L=\lim_{h\rightarrow 0}\frac{f(2+2h+h^2)-f(2)}{f(1+h-h^2)-f(1)}\)
Answer (Detailed Solution Below)
Evaluation of Limits Question 3 Detailed Solution
Evaluation of Limits Question 4:
\(\rm \lim_{x\rightarrow \infty}\{x-\sqrt[n]{(x-a)(x-a_2)...(x-a_n)}\}\) a1 a2, ... an ধনাত্মক মূলদ সংখ্যা, সীমা হল
Answer (Detailed Solution Below)
Evaluation of Limits Question 4 Detailed Solution
Evaluation of Limits Question 5:
যদি y = In(emx + e-mx ) হয়, তাহলে x = 0 এ \(\rm \frac{dy}{dx}\) এর মান কত?
Answer (Detailed Solution Below)
Evaluation of Limits Question 5 Detailed Solution
ধারণা:
যদি y = ln f(x) হয়, তাহলে \(\frac{dy}{dx}=\frac{f'(x)}{f(x)}\)
গণনা:
প্রদত্ত ফাংশন হল y = ln (emx + me-mx)
পার্থক্য করে পাই,
\(\frac{dy}{dx}=\frac{1}{e^{mx}+e^{-mx}}(me^{mx}-me^{-mx})\)
x = 0 এ, আমাদের আছে
\(\frac{dy}{dx}=\frac{1}{e^{0}+e^{0}}(me^{m0}-me^{-m0})\)
⇒ \(\frac{dy}{dx}=0\)
y = ln(e mx + me -mx ), \(\frac{dy}{dx}=0\) এর জন্য x = 0
Top Evaluation of Limits MCQ Objective Questions
\(\sqrt{3 + 2 \sqrt{2}}\) - \(\sqrt{3 - 2 \sqrt{2}}\) সমান:
Answer (Detailed Solution Below)
Evaluation of Limits Question 6 Detailed Solution
Download Solution PDFপ্রদত্ত:
\(X=\sqrt{3 + 2 \sqrt{2}}-\sqrt{3 - 2 \sqrt{2}}\)
\(=\sqrt {{(2 + 1) + 2} \sqrt 2}-\sqrt {{(2 + 1) - 2} \sqrt 2}\)
\(=\sqrt {{{{\left( {\sqrt 2 } \right)}^2} + {1^2}} + 2\sqrt 2}-\sqrt {{{{\left( {\sqrt 2 } \right)}^2} + {1^2}} - 2\sqrt 2}\)
\(=\sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}}-\sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}}\)
= √2 + 1 – (√2 – 1)
= 2
Evaluation of Limits Question 7:
\(\lim_{x\rightarrow 0} \frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}\) এর মান কত?
Answer (Detailed Solution Below)
Evaluation of Limits Question 7 Detailed Solution
গণনা
\(\lim \limits_{x\rightarrow 0} \dfrac{1-\cos 2x}{x(\tan 4x)}(3+\cos x)\)
⇒ \(\lim \limits_{x\rightarrow 0} 2\left(\dfrac{\sin x}{x}\right)^{2}.\dfrac{1}{4}\left(\dfrac{4x}{\tan 4x }\right)(3+\cos x)\)
⇒ \(2\times 1\times\dfrac{1}{4}\times 1\times(3+1)=2\)
অতএব, বিকল্প 3 সঠিক।
Evaluation of Limits Question 8:
\(\sqrt{3 + 2 \sqrt{2}}\) - \(\sqrt{3 - 2 \sqrt{2}}\) সমান:
Answer (Detailed Solution Below)
Evaluation of Limits Question 8 Detailed Solution
প্রদত্ত:
\(X=\sqrt{3 + 2 \sqrt{2}}-\sqrt{3 - 2 \sqrt{2}}\)
\(=\sqrt {{(2 + 1) + 2} \sqrt 2}-\sqrt {{(2 + 1) - 2} \sqrt 2}\)
\(=\sqrt {{{{\left( {\sqrt 2 } \right)}^2} + {1^2}} + 2\sqrt 2}-\sqrt {{{{\left( {\sqrt 2 } \right)}^2} + {1^2}} - 2\sqrt 2}\)
\(=\sqrt {{{\left( {\sqrt 2 + 1} \right)}^2}}-\sqrt {{{\left( {\sqrt 2 - 1} \right)}^2}}\)
= √2 + 1 – (√2 – 1)
= 2
Evaluation of Limits Question 9:
যদি y = In(emx + e-mx ) হয়, তাহলে x = 0 এ \(\rm \frac{dy}{dx}\) এর মান কত?
Answer (Detailed Solution Below)
Evaluation of Limits Question 9 Detailed Solution
ধারণা:
যদি y = ln f(x) হয়, তাহলে \(\frac{dy}{dx}=\frac{f'(x)}{f(x)}\)
গণনা:
প্রদত্ত ফাংশন হল y = ln (emx + me-mx)
পার্থক্য করে পাই,
\(\frac{dy}{dx}=\frac{1}{e^{mx}+e^{-mx}}(me^{mx}-me^{-mx})\)
x = 0 এ, আমাদের আছে
\(\frac{dy}{dx}=\frac{1}{e^{0}+e^{0}}(me^{m0}-me^{-m0})\)
⇒ \(\frac{dy}{dx}=0\)
y = ln(e mx + me -mx ), \(\frac{dy}{dx}=0\) এর জন্য x = 0
Evaluation of Limits Question 10:
\(\rm \lim_{n\rightarrow \infty}\left[\left(\frac{1}{2.3}+\frac{1}{2^2.3}\right)+\left(\frac{1}{2^2.3^2}+\frac{1}{2^3.3^2}\right)+....+\left(\frac{1}{2^n.3^n}+\frac{1}{2^{n+1}.3^n}\right)\right]\) এর মান
Answer (Detailed Solution Below)
Evaluation of Limits Question 10 Detailed Solution
Evaluation of Limits Question 11:
f(x) একটি অবকলন যোগ্য অপেক্ষক এবং f' (2) = 6, f(1) = 4 দেওয়া আছে।
সেক্ষেত্রে, \(\rm L=\lim_{h\rightarrow 0}\frac{f(2+2h+h^2)-f(2)}{f(1+h-h^2)-f(1)}\)
Answer (Detailed Solution Below)
Evaluation of Limits Question 11 Detailed Solution
Evaluation of Limits Question 12:
\(\rm \lim_{x\rightarrow \infty}\{x-\sqrt[n]{(x-a)(x-a_2)...(x-a_n)}\}\) a1 a2, ... an ধনাত্মক মূলদ সংখ্যা, সীমা হল