Give an elementary proof that lim n→∞:xn = 0 for 0 < x < 1. This m

Q: Let f(x) = log21 (10x + 60) - 15√√x.

A: f(x)=log21⁡(10x+60)−15x

Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x&gt;0 To show  log1+x=x−x22+x331+θx3 for 0&lt;θ&lt;1 and log1+x&lt;x−x22+x33…

Q: Assume you have functions f and g such that f(n) is O(g(n)). For each of the following statements,…

A:

Q: Find the equation of the vertical asymptote f(x) = log(x – 1)

A:

Q: Calculate the limit of log3 x as n – ∞ O 3 8

A: There should be correction in the question that x tending infinity.    As there is nowhere 'n'…

Q: Differentiate f(x) = log, (9 – 10x).

A:

Q: Let f(x) = x=") – (x²)*, x > 0. %3D -

A: We are given f(x)=xxx-xxx, x&gt;0. As per the question,  we need to solve f(x)=xxx-xxx≤0,   x&gt;0.

Q: For the functions f (x) = log₂ (x) and g(x) =log₂ (x - 1): a. Sketch the functions, identifying 4…

A: