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prove root 2 as irrational number
G raph y = sec ( x ) Solution: As with tangent we will have to avoid x's for which cosine is zero (recall that sec x =1/ cos x) Secant will not present at
a) Using Karnaugh map, show X': A'BC'D'+ ABC'D'+ A'BCD'+ ABCD' (b) If R is an equival
Find the sum of (1 - 1/n ) + (1 - 2/n ) + (1 - 3/n ) ....... upto n terms. Ans: (1 - 1/n ) + (1 - 2/n ) - upto n terms ⇒[1+1+.......+n terms] - [ 1/n + 2/n +....+
1/8 of the passengers of a train were children.If there were 40 children travelling in the train on a certain day,how many adults were there in that train that day?
Example of Trig Substitutions Evaluate the subsequent integral. ∫ √((25x 2 - 4) / x) (dx) Solution In this type of case the substitution u = 25x 2 - 4 will not wo
What is Angle Pairs in Parallel Lines ? Next, we introduce several angle pairs formed by transversals which are very important in our study of geometry. Alternate interior an
Extrema : Note as well that while we say an "open interval around x = c " we mean that we can discover some interval ( a, b ) , not involving the endpoints, such that a Also,
Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17) Ans: The required number is the HCF of the n
1. Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function δ(q0, a, λ) = {[q0, A]} δ(q0, λ , λ) = {[q1, λ]} δ(q0, b, A) = {[q2
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