How do you find the limit of #(1 - 1/x)^x# as x approaches
2015年7月4日 · The limit is 1/e lim_(xrarroo)(1-1/x)^x has the form 1^oo which is an indeterminate form. We will use logarithms and the exponential function. Now, (1-1/x)^x = e^(ln(1-1/x)^x) So …
What is the limit of(1+(1/x))^x as x approaches infinity? - Socratic
2016年8月6日 · Make the limit of (1+(1/x))^x as x approaches infinity equal to any variable e.g. y, k. and take the natural logarithm of both sides. y=lim_(x-oo)(1+(1/x))^x ln y ...
How do you use the Binomial Theorem to expand #(1 + x) ^ -1#?
2017年3月2日 · How do you use the Binomial Theorem to expand #(1 + x) ^ -1#? Precalculus The Binomial Theorem The Binomial Theorem. 1 Answer
How do you solve x^2+x+1=0? - Socratic
2015年4月11日 · You can use the standard formula which allows you to solve any quadratic equation, which is x_{1,2} = \frac{-b \pm \sqrt{b^2-4ac}}{2a} b^2-4ac, also called \Delta (delta), …
What is the limit of #(x/(x+1))^x # as x approaches infinity?
2016年3月21日 · Putting them together, we get our final result. #lim_(x->oo)(x/(x+1))^x = e^(lim_(x->oo)xln(x/(x+1))) = e^-1 = 1/e#
What is the limit of x^(1/x) as x approaches infinity? | Socratic
2016年4月6日 · lim_(xrarroo)x^(1/x) = 1 lim_(xrarroo)x^(1/x) = lim_(xrarroo)e^ln(x^(1/x)) = lim_(xrarroo)e^(1/xlnx) = e^(lim_(xrarroo)(1/xlnx)). And lim_(xrarroo)(1/xlnx) = lim ...
How do you find the derivative of #f(x)= x/(x-1)#? - Socratic
2016年12月23日 · To differentiate using the product rule, rewrite as f(x)=x(x-1)^-1 Product rule: f(x)=g(x)h(x) f'(x)=g(x)h'(x) + g'(x)h(x) In our case, g(x)=x and h(x)=(x-1)^-1 Leaving g(x) alone …
What is #lim_(x=>0^+)x^(1/x)# - Socratic
2017年3月2日 · Set #f(x)=x^(1/x)# then take logarithms on both sides. #lnf(x)=1/x*lnx# #f(x)=e^(lnx/x)# Now we must find the limit #lim_(x->0^+) lnx/x#. We observe that this is …
The limit of ln(x)/(x-1) as x approaches 1 equals what? - Socratic
2018年1月3日 · lim_(x->1)ln(x)/(x-1)=1 First, we can try directly pluggin in x: ln(1)/(1-1)=0/0 However, the result 0 \\/ 0 is inconclusive, so we need to use another method. In this case, my …
How do you factor x^2 + x +1? | Socratic
2016年7月27日 · can't be factored. y = x^2 + x + 1. D = d^2 - 4ac = 1 - 4 = - 3 Because D < 0 and is not a perfect square, this trinomial can't be factored.