&(a) \quad \text{Izračunaj: } \lim_{x \to 0} \frac{\ln(1+x)}{x} && \\ &(b) \quad \text{Riješi diferencijalnu jednadžbu: } y'' + 2y' + y = e^{-x}, \quad y(0) = 0, \, y'(0) = 1 && \\ &(c) \quad \text{Izračunaj: } \iint_D \left(x^2 + y^2\right) \, \mathrm{d}x \mathrm{d}y, \quad D = \{(x,y) \in \mathbb{R}^2 \mid x^2 + y^2 \leq 1\} && \\ &(d) \quad \text{Izračunaj: } \int_{-\infty}^{\infty} \frac{e^{-x^2/2}}{\sqrt{2\pi}} \, \mathrm{d}x && \\ &(e) \quad \text{Riješi sustav jednadžbi:} \begin{cases} x^2 + y^2 + z^2 &= 10 \\ x+y+z &= 0 \end{cases} && \\ &(f) \quad \text{Izračunaj: } \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} \frac{1}{\sqrt{k}} && \\ &(g) \quad \text{Riješi integralnu jednadžbu: } f(x) = \int_{0}^{x} \frac{t}{f(t)+1} \, \mathrm{d}t, \quad f(0) = 1 && \\ &(h) \quad \text{Izračunaj: } \text{Re } \int_{0}^{2\pi} \frac{e^{ix}}{3-e^{ix}} \, \mathrm{d}x && \\ &(i) \quad \text{Izračunaj: } \lim_{x \to 0} \frac{e^x - \sin x}{x^2} && \\ &(j) \quad \text{Izračunaj: } \lim_{x \to 1} \frac{x^2 + 2x - 3}{x^3 - 1} \\ &\textbf{Zadaci sa decimalnim brojevima} \\ &(a) \quad \lim_{x\to\infty} \left(\sqrt{x^2 + x} - \sqrt{x^2 - x}\right) \\ &(b) \quad \int_0^{\infty} e^{-x}\ln(x) dx \\ &(c) \quad \frac{d}{dx}\left(\frac{x^2 + 1}{\sqrt{1 - x^2}}\right) \\ &(d) \quad \int \frac{1 + \sin x}{\cos^2 x} dx \\ &(e) \quad \lim_{n\to\infty} \left(\frac{2^n}{n!}\right)^{1/n} \\ &(f) \quad \frac{d}{dx}\left[\left(\frac{1 - x}{1 + x}\right)^x\right] \\ &(g) \quad \int \frac{x}{\sqrt{1 + x^2}} dx \\ &(h) \quad \frac{d}{dx}\left(\ln\left[\frac{x^2 + 1}{\sqrt{x^2 + 2}}\right]\right) \\ &(i) \quad \int \frac{1 + \cos x}{\sin^2 x} dx \\