Question The function \( f(x)=\sqrt{-(x-2)^{2}+1} \) is graphed below. Use geometric formulas to evaluate the following definite integral. \[ \int_{1}^{2}\left(\sqrt{-(x-2)^{2}+1}\right) d x \] Enter an exact answer.

Find differenthal equation of the primitue \( x y+x^{2} y+y^{2}=13 \)

Jika \( m \) dan \( n \) adalah bilangan negatif dan berlaku \( \lim _{x \rightarrow n} \frac{4-\sqrt{m(x+n)}}{n-x}=n \), maka nilai dari \( m-n=\cdots \) (A) -9 (B) -7 (C) -5 (D) 7 (E) 9

4. Let \( g \) be a function such that \( g(1)=3 \) and whose derivative is \( g^{\prime}(x)=6 \cos (2 \pi x)+3 \). Solve analytically a. Use a linear approximation to estimate the value of \( g(1.2) \). b. Find the solution to the differential equation \( d g=(6 \cos (2 \pi x)+3) d x \)

5. Given \( h(x)=\int_{0}^{4 x} \sqrt{t-2} d t \), evaluate the following analytically. \( \begin{array}{ll}\text { a. Determine when } h(x)=\frac{16}{3} & \text { b. Determine when } h^{\prime}(x)=8\end{array} \)

Find equations of the tangent line and normal line to \( x^{2}+4 x y+y^{2}=13,(2,1) \)