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Evaluate \( \lim_{x \to 1} \dfrac{x^72x^5+1}{x^33x^2+2}\)
Evaluate \(\lim_{x \to 3} \dfrac{x^3+27}{x^5+243} \)
Evaluate \( \lim_{x \to \frac{\pi}{6}} \dfrac{\sqrt{3}\sin x\cos x}{x\frac{\pi}{6}}\)
Evaluate \(\lim_{x \to \frac{\pi}{3}}\dfrac{\sqrt{1\cos 6 x}}{\sqrt{2}\left( \dfrac{\pi}{3}x \right)} \)
Evaluate \( \lim_{x \to 0} \dfrac{1\cos m x}{1\cos nx}\)
Evaluate \(\lim_{x \to a} \dfrac{\sin x\sin a}{\sqrt{x}\sqrt{a}} \)
Evaluate \(\lim_{x \to \frac{\pi}{6}} \dfrac{\cot^2x3}{\csc x2} \)
Evaluate \( \lim_{x \to 0} \dfrac{\sin x2 \sin 3x+\sin 5x}{x}\)
If \(\lim_{x \to 1} \dfrac{x^41}{x1}=\lim_{x \to k} \dfrac{x^3k^3}{x^2k^2} \), then find \( k \).
Evaluate \(\lim_{x \to \frac{1}{2}} \left( \dfrac{8x3}{2x1}\dfrac{4x^2+1}{4x^21} \right) \)
Differentiate \( \dfrac{x^4+x^3+x^2+1}{x}\) at \( x=1\).
Differentiate \((\sec x1)(\sec x+1) \).
Differentiate \( (\sin x+\cos x)^2 \)
Differentiate \( x \cos x \)
\(\lim_{x \to \frac{\pi}{4}} \dfrac{\tan^3x\tan x}{\cos \left( x+\dfrac{\pi}{4} \right)} \) is equal to____
\(\lim_{x \to \pi} \dfrac{1\sin \dfrac{\pi}{2}}{\cos \dfrac{x}{2}\left( \cos \dfrac{x}{4}\sin \dfrac{x}{4} \right)} \) is equal to_______
\( \lim_{x \to \frac{x}{4}} \dfrac{x4}{x4}\); Evaluate it.
So limit does not exist
If \(f(x)=\begin{Bmatrix}
\dfrac{k \cos x}{\pi2x} &x \neq \dfrac{\pi}{2} \\
3,& x=\dfrac{\pi}{2}
\end{Bmatrix} \) and \( \lim_{x \to \frac{\pi}{4}} f(x)=f\left( \dfrac{\pi}{2} \right)\), then find the value of \( k \).
If \(f(x)=\begin{Bmatrix}
x+2, & x \leq 1 \\
cx^2,& x > 1
\end{Bmatrix} \), then find \( c \) when \( \lim_{x \to 1} f(x) \) exists.
Since exists, then
Solve: \( \lim_{x \to 0} \dfrac{(1+x)^n1}{x}\) is equal to______
\(\lim_{x \to 1} \dfrac{x^m1}{x^n1} \) is equal to_____
Solve: \(\lim_{\theta \to 0} \dfrac{1\cos 4 \theta}{1\cos 6\theta} \)
Evaluate: \( \lim_{x \to \frac{\pi}{4}} \dfrac{\sec^2 x2}{\tan x1}\)
Evaluate: \(\lim_{x \to 0} \dfrac{\csc x\cot x}{x} \)
\( \lim_{x \to 0} \dfrac{\sin x}{x}\) is equal to_____
So, limit does not exist.