;−∞∞e−x2dx=1满足了全概率为1的最基本条件。 拉伸一下x轴,就可以得到标准正态分布概率密度的函数表达式。 通过换元法, u=2xu=\sqrt{2}xu...=e−b2∫−∞∞e−x2dx=e−b2QA(b)=\int_{-\infty}^{\i
Evaluate integral_0^4 integral_0^4 - x x y dy dx. Evaluate: 1 0 d x ( 1 + x ) 4 Evaluate: -7 - (-5) -3. Evaluate 1. \int_{1}^{3} \frac{1}{x^2 - 4x + 5} dx 2. \int{x}^{3} \sin (x^2) dx Evaluate \lim_{x \rightarrow 2-} \frac{(x^2 - 5x + 6...
Correctly display e^x and d/dx in the functions virtual keyboard Ensure the correct spacing around fractions. In Safari, the fonts would not load. This was a regression due to a change in the behavior of the API to test if a font is loaded. Safari lies and always answer yes (to preve...
x is not equal to −2, then f(−2)= ___. Continuity:When we talk about continuity or say that a function is continuous at a certain point, we imply that the left-hand limit, the right-hand limit, and the value of the functio...
if f(2)=10,f′ is continuous, and ∫25f′(x)dx=19, what is the value of f(5)? The Fundamental Theorem of Calculus One part of the Fundamental Theorem of Calculus outlines a way to evaluate definite integrals. This method allows us to find ...
Find the reduction formula for the \int_0^{\frac{\pi}{2\sin^n (18x)dx. Suppose that A= D + E and that \frac{D}{A}= 0.80. Solve for \frac{D}{E}. Explain how you calculate 1.4929^(1/5). Derive a reduction formula for \int^∞ _0 x^...
Answer to: Assume that p,q are real numbers and f ( x ) = x ^2 + p x + q . Find real numbers alpha , beta such that f ( x ) = ( x - alpha )^ 2...
Set g(x) equals x to the power of 7 minus 5. Using the initial guess of x1 equals 4 and the recursion, iterate the recursion until xn agrees with seventh root of 5 to two decimal points Prove that 2^n greater than (n ...
Evaluate the definite interval \sqrt {(5x)} (\sqrt{(x)}+\sqrt{(5)} dx on the interval __(0,9)__ Given: f(x) = -|x+1|+4 Find the range of f(x) in interval notation. Determine the interval(s) on which the function is decreasing. A...
Calculate the derivation of y with respect to x. x^3y + 3xy^3 = x + y How do you do differentials? Derive a reduction formula for \int^∞ _0 x^n e^{-x} dx. How do you prove all spheres are similar? Let w = -3xy-2yz-4xz, x=st, y =e^{st}, z...