Maturità / Esame di Stato (Italy) · Mathematics

Calculus, Functions, Geometry, and Probability

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In mathematics, what is the derivative of the rational function $f (x) = \frac{2 x - 1}{x + 3}$ with respect to $x$ ?
In mathematics, what is the value of the limit $lim_{x \to 0} \frac{l n ( 1 + 4 x )}{s i n ( 2 x )}$ ?
In mathematics, which function represents the general solution of the first-order differential equation $y^{'} - 2 x y = x$ ?
In mathematics, what is the area of the region bounded by the parabola $y = 3 x - x^{2}$ and the $x$ -axis?
In mathematics, what is the radius of convergence $R$ of the power series $\sum_{n = 1}^{\infty} \frac{( 2 x - 1 ) ^{n}}{n \cdot 3 ^{n}}$ ?
In mathematics, what are the coordinates of the inflection point of the cubic curve $y = x^{3} - 3 x^{2} + 4$ ?
In mathematics, what is the value of the definite integral $\int_{0}^{π /2} x cos (x) d x$ ?
In mathematics, what is the equation of the tangent plane to the sphere $x^{2} + y^{2} + z^{2} = 9$ at the point $(1, 2, 2)$ ?
In mathematics, what is the horizontal asymptote of the function $f (x) = \frac{5 x ^{2} - 3 x + 1}{2 x ^{2} + 7}$ as $x \to \pm \infty$ ?
In mathematics, what is the probability of rolling a sum of exactly 7 with two fair, standard six-sided dice?
In mathematics, what is the maximum value of the function $f (x) = x e^{- 2 x}$ on the interval $[0, \infty)$ ?
In mathematics, what is the value of the determinant $2435$ ?
In mathematics, which test confirms the convergence of the infinite alternating series $\sum_{n = 1}^{\infty} \frac{( - 1 ) ^{n + 1}}{n}$ ?
In mathematics, what are the foci of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{16} = 1$ in Cartesian coordinates?
In mathematics, what is the sum of the infinite geometric series $6 + 2 + \frac{2}{3} + \frac{2}{9} + \dots$ ?
In mathematics, what is the value of the improper integral $\int_{1}^{\infty} \frac{1}{x ^{3}} d x$ ?
In mathematics, what is the amplitude and period of the sinusoidal function $f (x) = - 4 sin (3 x)$ ?
In mathematics, how many distinct four-letter arrangements can be formed from the letters of the word 'ROMA' without repetition?
In mathematics, what is the acute angle between the two lines $y = 3 x + 2$ and $y = \frac{1}{3} x - 4$ ?
In mathematics, what is the derivative of the exponential function $f (x) = 5^{2 x}$ with respect to $x$ ?
In mathematics, what is the value of $\int_{0}^{1} \frac{x}{x ^{2} + 1} d x$ ?
In mathematics, which value of $k$ makes the vectors $u = (2, - 3, 1)$ and $v = (k, 4, 6)$ perpendicular?
In mathematics, what is the volume of the solid generated by revolving the region under $y = x$ from $x = 0$ to $x = 4$ about the $x$ -axis?
In mathematics, what is the distance from the point $P (2, 3)$ to the line $3 x - 4 y + 1 = 0$ ?
In mathematics, what is the value of the limit $lim_{x \to 0} \frac{e ^{x^{2}} - 1}{1 - c o s ( 2 x )}$ ?
In mathematics, what is the third derivative $f^{'''} (x)$ of $f (x) = cos (2 x)$ ?
In mathematics, what is the solution set of the logarithmic inequality $lo g_{2} (x - 3) < 3$ ?
In mathematics, what is the value of the sum $\sum_{k = 1}^{n} (2 k - 1)$ for any positive integer $n$ ?
In mathematics, what is the domain of the real-valued function $f (x) = \frac{x - 1}{x + 2}$ ?
In mathematics, what is the curvature $κ$ of a circle of radius $R = 5$ at any point on its circumference?
In mathematics, if events $A$ and $B$ are independent with $P (A) = 0.4$ and $P (B) = 0.5$ , what is $P (A \cup B)$ ?
In mathematics, what is the coefficient of $x^{3}$ in the binomial expansion of $(2 x - 1)^{5}$ ?
In mathematics, what is the value of $arcsin (- \frac{3}{2})$ in principal branch radians?
In mathematics, which condition guarantees that a real symmetric matrix $A$ is positive definite?
In mathematics, what is the asymptote of the hyperbola $\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1$ with positive slope?
In mathematics, what is the value of the limit $lim_{x \to 1} \frac{x ^{3} - 1}{x ^{2} - 1}$ ?
In mathematics, what is the length of the arc of the curve $y = \frac{2}{3} x^{3/2}$ from $x = 0$ to $x = 3$ ?
In mathematics, what is the derivative of $f (x) = arctan (3 x)$ with respect to $x$ ?
In mathematics, what is the scalar product of the two vectors $a = 3 i - 2 j + 4 k$ and $b = i + 5 j - k$ ?
In mathematics, what is the general solution of the second-order homogeneous differential equation $y^{''} + 4 y^{'} + 4 y = 0$ ?
In mathematics, what is the median of the data set ${12, 5, 8, 20, 15, 9, 3}$ ?
In mathematics, what is the value of the complex expression $(1 + i)^{8}$ ?
In mathematics, what is the equation of the normal line to the curve $y = x^{2}$ at the point $(1, 1)$ ?

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