(28) \( \int \sin ^{5} x \sec x d x \)

Use Lagrange interpolation polynomial of degree 3 to estimate \( f(8.4) \) if \( f(8.1)=16.9441, f(8.3)=17.5649, f(8.6)=18.5052 \), and \( f(8.7)=18.8209 \) Verify that \( \sum_{i=0}^{3} L_{i}(8.4)=1 \)

1) \( y=\cos ^{-1}(\sin x) \Rightarrow y^{\prime}=? \) A) \( -\frac{\cos x}{|\cos x|} \) B) \( \frac{\cos x}{|\cos x|} \) C) \( -\frac{\cos x}{\sqrt{1-x^{2}}} \) D) \( \frac{\cos x}{\sqrt{1-x^{2}}} \) E) \( -\frac{\sin x}{\sqrt{1-x^{2}}} \)

11) \( f(x)=\left(x^{2}-4\right)^{2} \) fonksiyonunun artan olduğu aralıklar hangisidir? A) \( (-2,0) \) ve \( (2, \infty) \) B) \( (-2,0) \) ve \( (-\infty,-2) \) C) \( (-2,0) \) ve \( (0,2) \) D) \( (2, \infty) \) ve \( (-\infty,-2) \) E) \( (2, \infty) \) ve \( (0,2) \)

25) \( \lim _{x \rightarrow 0} \frac{|x-2|}{x-2}= \) ? \( \begin{array}{lllll}\text { A) }-\infty & \text { B) Limit yoktur } & \text { C) } 1 & \text { D) } \infty & \text { E) }-1\end{array} \)

to find the principal resistance values for optimizing power flow across the network. 1. In a distributed system, the latency \( L(x, y, z)=x^{2}+2 y^{2}+3 z^{2} \) (in milliseconds) depends on the numbe servers at locations \( x, y \), and \( z \). The total number of servers is constrained by \( x+y+z=20 \). Find the configuration of servers that minimizes latency.