Ex 2.1, 1 Find principal value of sin1 (1/2) Chapter 2
Say we want to find a value for x which makes this equal to i, so want cos(x) = 0 and sin(x) = 1. x = pi/2 is a value which satisfies this. So e^(i*pi/2) = i. So now that we have this seemingly more complicated way of writing i, we can substitute it for the base of our exponent and raise it to the power of i. So we get (e^(i*pi/2))^i.
Ex 5.5, 6 Differentiate (x + 1/x)^x + x^(1 + 1/x) Teachoo
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Ex 7.5, 23 (MCQ) Integrate dx / x (x^2 + 1) equals (A) log x 1/2
Algebra Simplify (x-i) (x+i) (x − i) (x + i) ( x - i) ( x + i) Expand (x−i)(x+i) ( x - i) ( x + i) using the FOIL Method. Tap for more steps. x⋅x+xi− ix−ii x ⋅ x + x i - i x - i i Simplify terms. Tap for more steps. x2 + 1 x 2 + 1
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3 Answers Sorted by: 12 The conclusion merely counts dimensions of vector spaces. However, it is not generally true. The most basic properties of matrix multiplication show that the linear transformation represented by the matrix H = X(X′X)−X′ H = X ( X ′ X) − X ′ satisfies
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Roman numeral, any of the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, standing respectively for 1, 5, 10, 50, 100, 500, and 1,000 in the Hindu-Arabic numeral system.
Ex 4.1, 1 Class 10 Check whether following are quadratic equations
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t. e. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has. where e is the base of the natural logarithm, i is the imaginary.
Limit of (1+1/x)^x as x approaches ∞
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Solve the quadratic equation x + 1x 1 + x 2x + 2 = 3,(x 1, 2)
2 Answers Sorted by: 9 For any r.v. X X I(X, X) = H(X). I ( X, X) = H ( X). To see this, put Y = X Y = X in I(X, Y) = H(X) − H(X|Y) I ( X, Y) = H ( X) − H ( X | Y) and use H(X|X) = 0. (∗) H ( X | X) = 0. ( ∗)
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