Choose the Correct options
0 of 25 questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 25 questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score 

Your score 

\( \lim_{x \to 0} \dfrac{\tan 2xx}{3x\sin x}\) is equal to_______
Evaluate: \( \lim_{x \to 1} \dfrac{(\sqrt{x}1)(2x3)}{2x^2+x3}\)
If \( f(x)=\begin{Bmatrix}
\dfrac{\sin [x]}{[x]}, &[x]\neq 0 \\
0, & [x]=0
\end{Bmatrix}\), then \(\lim_{x \to 0} f(x)\) is equal to______
So, limit does not exist
If \(f(x) =\begin{Bmatrix}
x^21, & 0< x <2 \\
2x+3, & 2 \leq x <3
\end{Bmatrix} \), then the quadratic equation whose roots are \(\lim_{x \to 2^} f(x) \) and \( \lim_{x \to 2^+} f(x)\) is_____
So, the quadratic equation whose roots are ย and is i.e.,
If \( f(x)=x[x]\), then \(f’\left( \dfrac{1}{2} \right) \) is_______
If \( y=\sqrt{x}+\dfrac{1}{\sqrt{x}}\), then \( \dfrac{dy}{dx}\Big _{x=1}\)ย is equal to_____
If \( f(x)=\dfrac{x4}{2\sqrt{x}}\), then \( f’ (1)\) is equal to______
Solve: \( \lim_{x \to 3^+} \dfrac{x}{[x]}\)
If \( y=\dfrac{\sin (x+9)}{\cos x}\)ย then \( \dfrac{dy}{dx}\Big _{x=0}\)ย is equal to_____
\( \lim_{x \to 0} \left( \sin mx \cdot \cot \dfrac{x}{\sqrt{3}} \right)=2\), then \( m\) equals______
Solve: \( \lim_{x \to \frac{\pi}{2}} \dfrac{\cot x\cos x}{(\pi2x)^3} \)
Solve: \( \lim_{x \to 0} \dfrac{\sin (\pi \cos^2 x)}{x^2}\)
Evaluate: \( \lim_{x \to 0} \dfrac{(1\cos 2x)(3+\cos x)}{x \tan 4x}\)
Find \(\lim_{h \to 0} \dfrac{f(2h+2+h^2)f(2)}{f(hh^2+1)f(1)} \), given \( f'(2) =6\) and \(f'(1)=4 \)
If \(\lim_{x \to 0} \dfrac{\left\{ (an)nx\tan x \right\}\sin x}{x^2}=0 \), where \( n \)ย is a nonzero real number, then \( a \)ย is equal to_____
The integer \( n \) for which \(\lim_{x \to 0} \dfrac{(\cos x1)(\cos xe^x)}{x^n} \)ย is a finite nonzero number, is______
Since, the above limit is finite, if i.e.,
Evaluate: \( \lim_{x \to 0} \dfrac{x\tan 2x2x\tan x}{(1\cos 2x)^2}\)
The value of \( \lim_{x \to 0} \dfrac{\sqrt{\dfrac{1}{2}(1\cos^2x)}}{x}\) is______
Hence
Limit does not exist
\( \lim_{n \to \infty} \left( \dfrac{1}{1n^2}+\dfrac{2}{1n^2}+…+\dfrac{n}{1n^2} \right)\) is equal to_____
If \(f(a)=2, ~~f'(a)=1, ~~~g(a)=1,~ g'(a)=2 \) then the value of \(\lim_{x \to a} \dfrac{g(x) f(a)g(a)f(x)}{xa} \) is______
If \( G(x) =\sqrt{25x^2}\), then \(\lim_{x \to 1} \dfrac{G(x)G(1)}{x1} \) has the value_____
Let \(L=\lim_{x \to 0} \dfrac{a\sqrt{a^2x^2}\dfrac{x^2}{4}}{x^4}, a > 0 \). If \( L \) is finite, then the value of \( L \) is______
Since, is finite
Evaluate: \(\lim_{h \to 0} \dfrac{\log (1+2h)2\log (1+h)}{h^2} \)
If \(f(x)=\begin{Bmatrix}
\sin x, &x \neq n \pi,n=0,\pm1,\pm 2… \\
2, & \text {otherwise}
\end{Bmatrix} \) and \( g(x)=\begin{Bmatrix}
x^2+1, &x \neq0 ,2 \\
4,& x=0\\
5,&x=2
\end{Bmatrix}\), then \(\lim_{x \to 0} g [f(x)]\) is_____
Now,
Evaluate: \( \lim_{x \to 1} (1x)\tan \dfrac{\pi x}{2}\)