当 x 趋近于 0 时,tan x ∼ x,sin x ∼ x,√(1-2x)-1 ∼ -x,cos x - 1 ∼ -(x^2)/2。将这些替换应用到原极限表达式中,得到: lim_(x → 0) (tan x - sin x)/((√(1-2x)-1)(cos x - 1)) ∼ lim_(x → 0) (x - x)/((-x) ⋅ (-(x^2)/2...
x^2 将简化后的分子和分母代入原极限表达式,并利用 sin x ∼ x,得到: lim_(x → 0) (1/2x^2 - 1/8x^4 + 1/4x^2 + o(x^3))/(x^2) = lim_(x → 0) (3/4 - 1/8x^2 + o(x)) = 3/4 因此,limlimits_(x→0)(√(1+x(sin)x)-√((cos)x))/((ln)(1+(tan)...
Evaluate the following limits: A) \lim_{x \rightarrow 0} \frac{\sin (12x)}{\tan (3x)} B) \lim _{x \rightarrow \frac{\pi}{2 3 \cos (-5x) \sec (7x) Evaluate the following limits, if it exist. (a) \lim _{x \rightarrow 5} \frac{x^{2}-7 x+10}{x-5}...
$$L = \lim_{x \to 1} \; \frac {\ln(x)}{\sin(\pi x)} \; \; \; \;... Learn more about this topic: Limit of a Function | Definition, Rules & Examples from Chapter 6/ Lesson 4 48K Develop an intuition for the limit of a func...
Stimulated by Jakobsen and Pellegrini's Love the Sin: Sexual Regulation and the Limits of Religious Tolerance, this essay is an effort to extend the value of their contribution by including a psychoanalytic perspective within its purview. My intent is to bring psychoanalytic readers into this ...
(5) 当 x 趋近于无穷大时,tan x 和 sin x 在有限范围内振荡,而 x 线性增长。因此,分子和分母都趋向于无穷大。使用洛必达法则,对分子分母求导后,得到 limlimits_(x→∞)(1 + cos x)。由于 cos x 在 x →∞ 时振荡,极限不存在。 (6) 分子和分母完全相同,因此在 x →∞时,它们的比值...
(1) 当 x →∞时,sin 9x ∼ 9x,sin 3x ∼ 3x,所以极限值为 (9x)/(3x) = 3。 (2) 当 x →∞时,tan 7x ∼ 7x,sin 4x ∼ 4x,所以极限值为 (7x)/(4x) = 7/4。 (3) 当 x →∞时,1 - cos x ∼ (x^2)/2,sin x ∼ x,所以极限值为 ((x^2)/2)/(x^2) = 1/...
\lim_{x \rightarrow 0} \frac{\sin 4x - 4x + \frac{32}{3} x^3}{x^5} Use series to evaluate the limit. \lim_{x \rightarrow \infty } x^2(e^\frac{3}{x^2} - 1) Use the series to evaluate t...
a) \lim\limits_{\theta \rightarrow \frac {\pi}{2 \frac {1 - \sin \theta}{1 + \cos \theta} b) \lim\limits_{x \rightarrow 1} \frac {x^6 - 1}{x^5 - 1} c) \lim\limits_{x \rightarrow \inf Find the limit lim_{x \rightarrow 0} \frac {[1/(x+...
Homosexuals, Heretics, and the Practice of Freedom Commentary on Love the Sin: Sexual Regulation and the Limits of Religious Tolerance by Janet R. Jakobsen and Ann PelligriniHere I construe Janet R. Jakobsen and Ann Pellegrini's proposal to protect freedom of sexual expression among consenting ...