(2 points) The area \(A\) of the region \(S\) that lies under the graph of the continuous function \(f\) on the interval \([a, b]\) is the limit of the sum of the areas of approximating rectangles:
$$ A=\lim _{n \rightarrow \infty}\left[f\left(x_{1}\right) \Delta x+f\left(x_{2}\right) \Delta x+\ldots+f\left(x_{n}\right) \Delta x\right]=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} f\left(x_{i}\right) \Delta x $$
where \(\Delta x=\frac{b-a}{n}\) and \(x_{i}=a+i \Delta x\).
The expression
$$ A=\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{\pi}{8 n} \tan \left(\frac{i \pi}{8 n}\right) $$
gives the area of the function \(f(x)=\) on the interval
(2 points) The area A of the region S that lies under the graph of the...
find an expression for the area of the region under the graph f(x)=x^4 on the interval [1,7]. use right-Hand endpoints as sample points choices1. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{7 i}{n}\right)^{4} \frac{7}{n}\)2. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{9 i}{n}\right)^{4} \frac{6}{n}\)3. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{6 i}{n}\right)^{4} \frac{6}{n}\)4. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{7 i}{n}\right)^{4} \frac{6}{n}\)5. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{6 i}{n}\right)^{4} \frac{7}{n}\)6. area \(=\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(1+\frac{9 i}{n}\right)^{4} \frac{7}{n}\)
(1 point) Definition: The AREA A of the region that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x)Ar + f(x2)Ax+... +f(x,y)Ax] 100 Wspacelin (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x3 from x = 0 to x = 2. 64 A. lim 7100 11 i= B....
-/2 POINTS SESSCALCET2 5.1.503.XP. The area A of the region that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. lim Rn limf ax + 2)Ax + ... + X)x] Use this definition to find an expression for the area under the graph off as a limit. Do not evaluate the limit. FX) - VX,15* $ 12 A lim Need Help? Talk to Tutor
The area A of the region S that les under the graph of the continuous fun the areas of approximating rectangles sthis deinition to find an expression for the area under the graph of f as a The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles Use this definition to find an expression for the area under the graph of f...
ssignment6: Problem 9 Previous Problem Problem List Next Problem (1 point) The area A of the region Sthat lies under the graph of the continuous function f on the interval (a, b) is the limit of the sum of the areas of approximating rectangles: A = lim (f(21)Ar + f(x2)Ax+...+f(xn)Ax] = lim f(x;)Az, n-> ng i=1 where Ax = b and Ti = a +iAr. The expression A = lim Itan(n) 7200 6n2 gives the area of the function f(x)...
Consider a discrete time signal \(y[n]=\frac{\sin (\pi n / 5)}{\pi n}+\cos (\pi n / 10) .\) Let's build the continuous time representation of \(y[n]\) using \(T_{s}=1 / 10\) as follows:$$ y_{\delta}(t)=\sum_{n=-\infty}^{\infty} y[n] \delta\left(t-n T_{s}\right)=\sum_{n=-\infty}^{\infty} y[n] \delta(t-n / 10) $$Choose the right expression for \(Y_{\delta}(j \omega)\).(Hint: You can first sketch \(Y\left(e^{j \Omega}\right)\). Then, you can obtain the sketch of \(Y_{\delta}(j \omega)\) from \(Y\left(e^{j \Omega}\right)\). Note that in the earlier lecture on sampling, we derived that \(Y_{\delta}(j \omega)=\left.Y\left(e^{j \Omega}\right)\right|_{\Omega=\omega T_{x}}=Y\left(e^{j \omega T_{\nu}}\right)\).In...
send help for these 4 questions, please show steps Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x)Ax +f(x2)Ax+...+f(x)Ax] - 00 Consider the function f(x) = x, 13x < 16. Using the above definition, determine which of the following expressions represents the area under the graph off as a limit. A. lim...
\(\mathrm{T}\) is a failure time following a Weibull distribution. Consider \(\mathrm{Y}=\log \mathrm{T}\) where \(\mathrm{Y}\) has an extreme value distribution with survival function$$ S_{Y}(y)=e^{-\epsilon^{\frac{n \mu}{\sigma}}} $$where \(-\infty<\mu<\infty\) is the location parameter and \(\sigma>0\) is the scale parameter. Expressing with parameters \(\mu\) and \(\varphi=\log \sigma\). Assume that failure times of subjects under study arise from Weibull distribution. Let \(x_{1}, \ldots, x_{n}\) be the observed failure or right censoring times for n subjects. Each subject i (i = \(1, \ldots, \mathrm{n}\) ) has...
Estimate the area Upper A between the graph of the function f left-parenthesis x right-parenthesis equals 1 0 s i n x and the interval left-bracket 0 comma pi right-bracket Number . Use an approximation scheme with n equals 2 comma 5 and 10 rectangles. Use the right endpoints. If your calculating utility will perform automatic summations, estimate the specified area using n equals 50 and n equals 100 rectangles.
Let X equal the larger outcome when a pair of 6-sided dice are rolled.(a) Assuming the two dice are independent, show that the probability function of \(X\) is \(f(x)=\frac{2 x-1}{36} \quad x=1, \ldots, 6\)(b) Confirm that \(f(x)\) is a probability function.(c) Find the mean of \(X\).(d) Can you generalise \(E(X)\) to a pair of fair \(m\) -sided dice?\(\left[\right.\) Hint: recall that \(\sum_{i=1}^{n} i=n(n+1) / 2\) and \(\left.\sum_{i=1}^{n} i^{2}=n(n+1)(2 n+1) / 6\right]\)