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}...
\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...
D3D12 - DXIL 16bit Types Test - Sin instruction D3D12 - DXIL 16bit Types Test - Sqrt instruction D3D12 - DXIL 16bit Types Test - Tan instruction D3D12 - DXIL 16bit Types Test - UAdd instruction D3D12 - DXIL 16bit Types Test - UMad instruction D3D12 - DXIL 16bit Types Test - UM...
将tan x写为(sin x)/(cos x),即lim_(x→0)(sin x)/(xcos x)。 已知lim_(x→0)(sin x)/x=1且cos x→1,因此极限为1⋅1=1。 出题点2:lim_(x→0)(sin x)/(sin2x) 分子sin x等价于x,分母sin2x等价于2x。 代入等价无穷小得lim_(x→0)x/(2x)=1/2,题目原答案1错误,正确答案为1...
(1) 当 x → 0 时,tan x ∼ x,sin x ∼ x,因此极限值为 1/2。 (2) 利用洛必达法则,极限值为 1/t。 (3) 题目表述可能存在错误,假设 x' 指的是 x,利用洛必达法则,极限值为 0。 (4) 直接代入 x=0,极限值为 1。 答案 (1) 1/2 (2) 1/t (3) 0 (4) 1...
$$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...
Evaluate: (1) \int_{0}^{1}\int_{x^{2^{x^{\frac{1}{4}\left(x^{\frac{1}{2 - y^{2}\right)dydx (2) \int_{0}^{\pi}\int_{0}^{\sin x}\left[1 + \cos x\right]dydx Evaluate \lim\limits_{x \rightarrow - \infty} \frac {-x^2}{3x^5}. ...
\lim_{x \rightarrow 0} \frac {\sin x (1 - \cos x)}{x^3} Evaluate the following limit. \lim_{x \rightarrow 4} \frac {\sqrt{x} - 2}{x^2 - 16} Evaluate the following limit. \lim_{x \rightarrow 0} \frac {2^x - 3^x}{x} Evaluate the following lim...