Why is infinity to the zero power indeterminant? Explain using an example why an absolute value can never be negative? Why infinity is equal to two times infinity? Explain why: a. \int^1_{-1} x^n dx = 0, when n is a positive, odd integer, and b. \int^1_{-1} x^n dx = ...
Why is L hospital's rule useful for finding the limits? So, L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit. Is Infinity over 0 indeterminate? Anoth...
The limit of the function f(x) = (x^3 - 9x + 3x^2)/(3x - 4 + 5x^2) as x approaches negative infinity is equal to zero. Is it true or false? If limit (x tends to infinity) f(x) exists, then f(x) must have a horizontal asymptote. True or false?
Find the limit, if it exists. If the limit does not exist, explain why. {eq}\lim_{x \to 0} \frac {1 - \cos 4x}{9x^2} {/eq} Existence of L'Hopital's Rule: There is interesting information regarding the existence of L'Hopital's rule. ...
Three conditions must be satisfied for helicopter money always to boost aggregate demand. First, there must be benefits from holding fiat base money other than its pecuniary rate of return. Second, fiat base money is irredeemable – viewed as an asset by the holder but not as a liability by...
So, since = 1, that means that = 1. High School Teacher: Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that . The variable x having a value close to zero is different than it having a value of exactly zero. It turns out that is un...
1. Introduction Quantum mechanics is known to be resistant to a realist understanding, as it is unclear what picture of reality it provides us. Nonetheless, a variety of realist quantum theories have been proposed, and among these, one finds the many-worlds theory, also known as Everettian qu...
For nonzeroz, write z = r*exp(i*t), wherer>0 andiis the imaginary unit. The choice oftis indeterminate, but we will have log(z) = log(r) + i*t for one of the possible values oft. Aszgoes to zero, log(z) goes to minus infinity no matter what the direction of approach. ...