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\[\lim_{x \to 0} \frac{5^x - 1}{\sqrt{4 + x} - 2}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\log \left( 1 + x \right)}{3^x - 1}\]
Concept: undefined >> undefined
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\[\lim_{x \to 0} \frac{a^x + a^{- x} - 2}{x^2}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{a^{mx} - 1}{b^{nx} - 1}, n \neq 0\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{a^x + b^x - 2}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{9^x - 2 . 6^x + 4^x}{x^2}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{8^x - 4^x - 2^x + 1}{x^2}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{a^{mx} - b^{nx}}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{a^x + b^x + c^x - 3}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 2} \frac{x - 2}{\log_a \left( x - 1 \right)}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{5^x + 3^x + 2^x - 3}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to \infty} \left( a^{1/x} - 1 \right)x\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{a^{mx} - b^{nx}}{\sin kx}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{a^x + b^ x - c^x - d^x}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{e^x - 1 + \sin x}{x}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{\sin 2x}{e^x - 1}\]
Concept: undefined >> undefined
\[\lim_{x \to 0} \frac{e\sin x - 1}{x}\]
Concept: undefined >> undefined
Find the standard deviation for the following data:
| x : | 3 | 8 | 13 | 18 | 23 |
| f : | 7 | 10 | 15 | 10 | 6 |
Concept: undefined >> undefined
Calculate the mean and S.D. for the following data:
| Expenditure in Rs: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency: | 14 | 13 | 27 | 21 | 15 |
Concept: undefined >> undefined
Calculate the standard deviation for the following data:
| Class: | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 |
| Frequency: | 9 | 17 | 43 | 82 | 81 | 44 | 24 |
Concept: undefined >> undefined
