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\[\lim_{x \to 1} \left( 1 - x \right) \tan \left( \frac{\pi x}{2} \right)\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{4}} \frac{1 - \tan x}{1 - \sqrt{2} \sin x}\]
Concept: undefined >> undefined
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\[\lim_{x \to \pi} \frac{\sqrt{2 + \cos x} - 1}{\left( \pi - x \right)^2}\]
Concept: undefined >> undefined
\[\lim_{x \to \pi} \frac{1 + \cos x}{\tan^2 x}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{2}} \left( \frac{\pi}{2} - x \right) \tan x\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{6}} \frac{\cot^2 x - 3}{cosec x - 2}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{4}} \frac{\sqrt{2} - \cos x - \sin x}{\left( 4x - \pi \right)^2}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{2}} \frac{\left( \frac{\pi}{2} - x \right) \sin x - 2 \cos x}{\left( \frac{\pi}{2} - x \right) + \cot x}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{4}} \frac{\cos x - \sin x}{\left( \frac{\pi}{4} - x \right) \left( \cos x + \sin x \right)}\]
Concept: undefined >> undefined
Evaluate the following limit:
\[\lim_{x \to \pi} \frac{1 - \sin\frac{x}{2}}{\cos\frac{x}{2}\left( \cos\frac{x}{4} - \sin\frac{x}{4} \right)}\]
Concept: undefined >> undefined
\[\lim_{x \to \pi} \frac{1 + \cos x}{\tan^2 x}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{4}} \frac{{cosec}^2 x - 2}{\cot x - 1}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{6}} \frac{\cot^2 x - 3}{cosec x - 2}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{\pi}{4}} \frac{2 - {cosec}^2 x}{1 - \cot x}\]
Concept: undefined >> undefined
\[\lim_{x \to \pi} \frac{\sqrt{2 + \cos x} - 1}{\left( \pi - x \right)^2}\]
Concept: undefined >> undefined
\[\lim_{x \to \frac{3\pi}{2}} \frac{1 + {cosec}^3 x}{\cot^2 x}\]
Concept: undefined >> undefined
Table below shows the frequency f with which 'x' alpha particles were radiated from a diskette
| x : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| f : | 51 | 203 | 383 | 525 | 532 | 408 | 273 | 139 | 43 | 27 | 10 | 4 | 2 |
Calculate the mean and variance.
Concept: undefined >> undefined
Write the variance of first n natural numbers.
Concept: undefined >> undefined
If x1, x2, ..., xn are n values of a variable X and y1, y2, ..., yn are n values of variable Y such that yi = axi + b; i = 1, 2, ..., n, then write Var(Y) in terms of Var(X).
Concept: undefined >> undefined
If a variable X takes values 0, 1, 2,..., n with frequencies nC0, nC1, nC2 , ... , nCn, then write variance X.
Concept: undefined >> undefined
