Asymptote — Breath Math

Asymptote is a straight line that continually approaches a given curve but does not meet it at any finite distance. A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes. The degree of the numerator and degree of the denominator determine whether or not there are any horizontal or […]

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Permutation and Combination – Class XI – Exercise 7.1 — Breath Math

1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) Repetition of the digits is allowed? (ii) Repetition of the digits is not allowed? Solution: (i) There will be number of ways of filling 3 vacant places in succession by the given five digits. Here, […]

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Principle of Mathematical Induction – Class XI – Exercise 4.1[Part 2] — Breath Math

11: Prove the following by using the principle of mathematical induction for all n€ N: 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + … +1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2) Solution: Let the given statement be P(n), i.e., P(n): 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + … +1/n(n+1)(n+2) = n(n+3)/4(n+1)(n+2) For n = 1, we have P(1): 1/1.2.3 = 1.(1+3)/4(1+1)(1+2) = […]

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Trigonometry Functions – Class XI -Exercise 3.1 — Breath Math

Find the radian measures corresponding to the following degree (i) 25˚ (ii) -47˚30’ (iii) 240˚ (iv) 520˚ Solution: (i) 25˚ We know that 180˚ = π radian 25˚ = π/180 x 25radian = 5π/36 radians (ii) -47˚30’ -47˚30’ = -471/2 = -95/2 degree -95/2 degree = π/180 x -95/2 radians = (-19/36×2) π radian = […]

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