$$ \begin{flalign*} & \textbf{Tasks - Gradište Elementary School - Lower Grades} && \\ &(a) \quad \text{Calculate:} \\ & \quad \frac{ §§V1(10,50,10)§§ }{4} \cdot \left(\frac{ §§V2(1,10,1)§§ }{6} + \frac{7}{ §§V3(1,10,1)§§ }\right) && \\ &(b) \quad \text{Solve the differential equation:} \\ & \quad y' + §§V3(1,10,1)§§ xy = x, \text{ for } y(0) = §§V2(1,5,1)§§ && \\ &(c) \quad \text{Calculate the integral:} \\ & \quad \int_{0}^{\pi} \sin(x) \cos(x) \,dx && \\ &(d) \quad \text{Find the inverse matrix:} \\ & \quad \text{Let } A = \begin{bmatrix} §§V3(1,10,1)§§ & §§V6(-10,0,1)§§ \\ 3 & §§V3(1,10,1)§§ \end{bmatrix}. \text{ Determine } A^{-1}. && \\ &(e) \quad \text{Solve the system of differential equations:} \\ & \quad \begin{cases} x' = -2x + §§V3(1,10,1)§§ y \\ y' = §§V3(1,10,1)§§ x - y \end{cases} && \\ &(f) \quad \text{Calculate the limit:} \\ & \quad \lim_{{x \to 0}} \frac{e^x - §§V6(1,10,1)§§ }{x} && \\ &(g) \quad \text{Expand the function in a Taylor series:} \\ & \quad f(x) = \ln(x+1), \text{ around } x = 0. && \\ &(h) \quad \text{Calculate the triple integral:} \\ & \quad \iiint_{V} (x^2 + y^2 + z^2) \,dx\,dy\,dz, \text{ where } V \text{ is the sphere } x^2 + y^2 + z^2 \leq 1. && \\ &(i) \quad \text{Solve the Laplace equation:} \\ & \quad \nabla^2 u = 0, \text{ in cylindrical coordinates,} \\ & \quad \text{with the condition } u(0, \theta, z) = \sin(2\theta). && \\ &(j) \quad \text{Calculate:} \\ & \quad \sum_{k=1}^{n} k^3, \text{ for } n \in \mathbb{N}. && \\ &(k) \quad \text{Find the singular values of the matrix:} \\ & \quad \text{Let } B = \begin{bmatrix} 1 & §§V3(1,10,1)§§ & 3 \\ 0 & §§V3(1,10,1)§§ & 4 \end{bmatrix}. \text{ Determine the singular values.} && \\ &(l) \quad \text{Solve the complex equation:} \\ & \quad z^4 - §§V5(1,10,1)§§ z^2 + §§V4(1,10,1)§§ = 0. && \\ &(m) \quad \text{Calculate the Fourier transformation:} \\ & \quad F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} \,dt, \text{ for } f(t) = e^{-|t|}. && \\ &(n) \quad \text{Find local maxima and minima of the function:} \\ & \quad f(x) = x^3 - §§V3(1,10,1)§§ x^2 + §§V3(10,100,1)§§ x + 2. && \\ &(o) \quad \text{Solve the vector equation:} \\ & \quad \mathbf{A} \cdot \mathbf{x} = \mathbf{b}, \text{ for } \mathbf{A} = \begin{bmatrix} 1 & -2 & 3 \\ 0 & 1 & -1 \\ 2 & 1 & 0 \end{bmatrix}, \mathbf{b} = \begin{bmatrix} 4 \\ -1 \\ 3 \end{bmatrix}. && \\ &(p) \quad \text{Calculate:} \\ & \quad \frac{d}{dx} \left( §§V3(1,10,1)§§ x^2 + 2\sqrt{x} \right), \text{ for } x > 0. && \\ &(q) \quad \text{Solve the system of nonlinear equations:} \\ & \quad \begin{cases} x^2 + y^2 = 10 \\ e^x + y = 8 \end{cases} && \\ &(r) \quad \text{Calculate the Riemann sum:} \\ & \quad \sum_{i=1}^{n} \frac{1}{n} \sin\left( \frac{i}{n} \pi \right), \text{ for } n \in \mathbb{N}. && \\ &(s) \quad \text{Find the extremum of the function:} \\ & \quad f(x,y) = x^2 + §§V3(1,10,3)§§ xy - §§V3(1,10,1)§§ y^2, \text{ on } D = \{(x,y) \mid x^2 + y^2 \leq 4\}. && \\ \end{flalign*} $$