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Rolle's Theorem
Assume f(x) is a function which satisfies all of the following.
1. f(x) is continuous in the closed interval [a,b].
2. f(x) is differentiable in the open interval (a,b).
3. f(a) = f(b)
So, there is a number c as a < c < b and f′(c) = 0. Or, though f(x) has a critical point in (a,b).
Method In this method we eliminate either x or y, get the value of other variable and then substitute that value in either of the original equations to
Find the sum of all natural no. between 101 & 304 which are divisible by 3 or 5. Find their sum. Ans: No let 101 and 304, which are divisible by 3. 102, 105..........
shapes
Determine if the following sequences converge or diverge. If the sequence converges find out its limit. a. {3n 2 - 1 / 10n + 5n 2 } ∞ n =2 b. {e 2n / n} ∞ n =1 c
The following table given the these scores and sales be nine salesman during last one year in a certain firm: text scores sales (in 000''rupees) 14 31 19
Differentiate following functions. (a) f ( x ) = 2 x 5 cosh x (b) h (t ) = sinh t / t + 1 Solution (a) f ′ ( x ) = 10x 4 cosh x + 2x 5 sinh x (b) h′ (t ) = (t
Hypergeometric Distribution Consider the previous example of the batch of light bulbs. Suppose the Bernoulli experiment is repeated without replacement. That is, once a bulb is
Expand (1- 1/2x -x^2)^9
what is the answer in skills bank
Probability Distribution for Continuous Random Variables In a continuous distribution, the variable can take any value within a specified range, e.g. 2.21 or 1.64 compared to
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