limits and infinity

If x is a variable such that it can take any real value how much ever If x is a variable such that it can take any real value how much eve..

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Limits at infinity: If x is a variable such that it can take any real value how much ever The two important properties of these one-sided limits that i) If the left hand limit and right hand limit of a function at a point exists, ..

>(iii) Let the gas be heated and allowed to expand. Suppose, in this case, the 'fall in temperature due to expansion' is less than the 'rise in temperature due to heat supplied', the net effect is a rise in the temperature of the gas. Therefore D T is positive. Thus is positive. (iv) Let the gas be..

Use the Limit Comparison Test to determine whether the series ∑ n=1 ∞ tan ( 1 n 2 ) is convergent or divergent. => divergent or convergent or cannot be determined..

Use Limit Comparison Test to determine whether the series ∑ n=1 ∞ 2 sin ( 1 n 4 ) is convergent or divergent. => convergent or oscillating or cannot be determined or divergent..

Use the Limit Comparison Test to determine whether the series ∑ n=1 ∞ 1 n 2 - 1 is convergent or divergent. => cannot be determined or convergent or divergent..

Express the limit lim n → ∞ ∑ i=1 n ( 3 n ) [( 3 i n ) 2 - 1] as a definite integral. => ∫ 0 1 x ( x 2 - 1) dx or ∫ 1 3 ( x 2 - 1) dx or ∫ 0 3 x ( x 2 - 1) dx or ∫ 0 3 ( x 2 - 1) dx ..

Use the limit comparison test to determine whether the series ∑ n=1 ∞ n ² 3 n 5 + 3 converges or diverges. => converges or cannot be determined or neither converges nor diverges or diverges..

Use the Limit Comparison Test to determine whether the series ∑ n=1 ∞ ( e 2 n - 1 ) is convergent or divergent. => cannot be determined or divergent or convergent..