Table of Contents
How do you prove that X is an even number?
(True) Proof: Let x be an odd number. This means that x = 2n+ 1 where n is an integer. If we square x we get: x 2= (2n+ 1) = (2n+ 1)(2n+ 1) = 4n2 + 4n+ 1 = 2(2n2 + 2n) + 1 which is of the form 2( integer ) + 1, and so is also an odd number. (b) y is an even number )y3 is an even number.
What is Euler’s formula for cos 1 sin 2?
The central mathematical fact that we are interested in here is generally called Euler’s formula”, and written ei= cos+ isin Using equations 2 the real and imaginary parts of this formula are cos= 1 2 (ei+ e i) sin= 1 2i (ei e i) (which, if you are familiar with hyperbolic functions, explains the name of the hyperbolic cosine and sine).
What is Cos and sin in denition?
De nition (Cosine and sine). Given a point on the unit circle, at a counter-clockwise angle from the positive x-axis, cos is the x-coordinate of the point. sin is the y-coordinate of the point. The picture of the unit circle and these coordinates looks like this: 1
What is the difference between cosine and sine?
De\fnition(Cosine and sine). Given a point on the unit circle, at a counter-clockwise anglerom the positivex-axis, cos is thex-coordinate of the point. sins they-coordinate of the point. The picture of the unit circle and these coordinates looks like this:
How do you prove that lim x → ∞(2 + 1 x) = 2?
Use the formal definition of limit at infinity to prove that lim x → ∞(2 + 1 x) = 2. Let ε > 0. Let N = 1 ε. Therefore, for all x > N, we have |2 + 1 x − 2| = |1 x| = 1 x < 1 N = ε.
What is the limit as x approaches -∞ of f(x)?
We say the limit as x approaches −∞ of f(x) is 2 and write lim x → – ∞f(x) = 2. Figure 4.40 The function approaches the asymptote y = 2 as x approaches ±∞. More generally, for any function f, we say the limit as x → ∞ of f(x) is L if f(x) becomes arbitrarily close to L as long as x is sufficiently large.
Is the volume of the region about the x-axis infinite?
In conclusion, although the area of the region between the x -axis and the graph of f(x) = 1/x over the interval [1, +∞) is infinite, the volume of the solid generated by revolving this region about the x -axis is finite. The solid generated is known as Gabriel’s Horn. Visit this website to read more about Gabriel’s Horn.