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Expansion Standard Series : Find the series expansion of log(1+x) power of x. Hence Prove that log x = $ (x-1) - \frac{1}{2}(x-1)^2 + \frac{1}{3}(x-1)^3\ldots $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Expansion Standard Series : Prove that log($ 1-x+x^2 ) \; = \; -x + \frac{x^2}{2} + \frac{2x^3}{3} $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Expansion Standard Series : Expand $log(1+x+x^2+x^3) \; in \; powers \; of \; x \; upto \; x^8 $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Expansion Standard Series $Show \; that \; log[ 1 \; + \; sin \; x] \; = \; x \; - \; \frac{x^2}{2} \; + \; \frac{x^3}{6} \; + \; \ldots $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Relation between circular and hyperbolic function : If $tan \frac{x}{2} \; = \; tanh\frac{u}{2}$ , then show that u = $log \; tan \Big( \frac{\pi}{4} + \frac{x}{2}\Big)$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Relation between circular and hyperbolic function : If tanh$ \; x = \frac{2}{3}$ , find the value of $x$ and then cosh $2x $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Relation between circular and hyperbolic function : Prove that $sec \;h^{-1}(sin\theta) = log(cot(\theta/2))$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Relation between circular and hyperbolic function : Prove $ \tfrac{1}{ 1 - \tfrac{1}{1 - \tfrac{1}{cosh^2 x}} } = cosh^2 x $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Relation between circular and hyperbolic function : If cosh $x$ = sec$\theta$ , prove that $x$ = log(sec$\theta$ + tan$\theta$ )
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Relation between circular and hyperbolic function : If $\alpha$ + $\iota\beta$ = tanh($\chi$ + $\iota \frac{\pi}{4}$) , prove that $\alpha^2 + \beta^2$ = 1
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Given L= {1,2,4,5,10,20} with divisibility relation.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Show that. ............................
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Simplify as sum of product
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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i. Draw a complete graph of 5 vertices.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Let G be a group of all permutations of degree 3 on 3 symbol 1,2,&3. Let H = {I,(1,2)} be a subgroup of G.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Give an example of graph which has
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Write the following permutations as the product of disjoint cycle.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Show that G=[1,-1,i,-i] is a group under usual multiplication of complex number.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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i) The average marks scored by 32 boys is 72 with standard deviation of 8 while that for 36 girls is 70 with standard deviation of 6. Test at 5% los whether the boys perform better than the girls.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Calculate the coefficient of correlation between x & y from the following data.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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The following table gives the number of accidents in a city during a week. Find whether the accidents are uniformly distributed over a week.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Given two lines of regression lines, 6y= 5x +90, 15x = 8y+130.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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It was found that the burning life of electric bulbs of a particular brand was normally distributed
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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Derive the MGF of binomial distribution and hence finds it's mean and variance.
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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A random discrete variable x has the probability mass function given,
engineering mathematics updated 5.7 years ago by parviagrawal100 • 0
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