计算极限
lim x → ∞ ( 3 x + 9 x ) 1 x , lim y → 0 + lim x → 0 + ln ( 2 x + e − y ) x 3 + y 2 , lim x → ∞ ln ( 1 + 1 x ) a r c c o t x , lim x → 0 1 − 1 − x 2 e x − cos x \lim_{x \rightarrow \infty}\left( 3^{x} + 9^{x} \right)^{\frac{1}{x}},\lim_{y \rightarrow 0^{+}}{\lim_{x \rightarrow 0^{+}}\frac{\ln{(2x + e^{- y})}}{\sqrt{x^{3} + y^{2}}}},\\ \lim_{x \rightarrow \infty}\frac{\ln{(1 + \frac{1}{x})}}{arccot \, x},\lim_{x \rightarrow 0}\frac{1 - \sqrt{1 - x^{2}}}{e^{x} - \cos x} x→∞lim(3x+9x)x1,y→0+limx→0+limx3+y2ln(2x+e−y),x→∞limarccotxln(1+x1),x→0limex−cosx1−1−x2
代码:
syms x y;
ans1 = limit((3^x+9^x)^(1/x),x,inf)
temp1 = limit(log(2*x+exp(-y))/(sqrt(x^3+y^2)-1),x,0);
ans2 = limit(s1,y,0)
ans3 = limit(log(1+1/x)/acot(x),x,inf)
ans4 = limit((1-sqrt(1-x^2))/(exp(x)-cos(x)),x,inf)
输出:
ans1 = 9
ans2 = 0
ans3 = 1
ans4 = 0