ENADE Matemática Practice Questions - ENADE Matemática - Exame Nacional de Desempenho dos Estudantes Exam - ENADE Matemática Practice Questions - ENADE Matemática - Exame Nacional de Desempenho dos Estudantes Exam

Question 1

Consider the real sequence defined by $a_n = \left(1 + \frac{3}{n}\right)^{2n}$ for $n \in \mathbb{N}^*$. What is the limit $L = \lim_{n \to \infty} a_n$?

$$e^6$ $$e^5$ $$e^3$ $$e^2$

Correct Answer:

$$e^6$

Question 2

Determine the radius of convergence $R$ and the open interval of convergence of the power series $\sum_{n=1}^\infty \frac{(3x - 1)^n}{n 4^n}$.

$$R = \frac{4}{3}$ and interval $\left(-\frac{4}{3}, \frac{4}{3}\right)$ $$R = 4$ and interval $(-1, 5)$ $$R = \frac{4}{3}$ and interval $\left(-1, \frac{5}{3}\right)$ $$R = \frac{3}{4}$ and interval $\left(-\frac{1}{2}, \frac{7}{6}\right)$

Correct Answer:

$$R = \frac{4}{3}$ and interval $\left(-1, \frac{5}{3}\right)$

Question 3

Calculate the directional derivative of the scalar field $f(x,y,z) = x^2 y - y z^2 + 2xz$ at the point $P(1, -1, 2)$ in the direction of the vector $\vec{v} = (2, -1, 2)$.

$$\frac{10}{3}$ $$\frac{19}{3}$ $$19$ $$\frac{8}{3}$

Correct Answer:

$$\frac{19}{3}$

Question 4

Let $f: [0,1] \to \mathbb{R}$ be Thomae's function (also known as the modified Dirichlet function), defined by $f(x) = 1/q$ if $x = p/q \in \mathbb{Q}$ is in lowest terms ($p \ge 0, q > 0$), $f(0) = 1$, and $f(x) = 0$ if $x \in [0,1] \setminus \mathbb{Q}$. Which of the following statements correctly characterizes the Riemann integrability and integral of $f$ on $[0,1]$?

$$f$ is not Riemann integrable on $[0,1]$ because it is discontinuous on all rational numbers in $[0,1]$. $$f$ is Riemann integrable on $[0,1]$ and its integral equals $1$. $$f$ is continuous everywhere on $[0,1]$, hence Riemann integrable with integral $1/2$. $$f$ is Riemann integrable on $[0,1]$ and $\int_0^1 f(x) dx = 0$ because the set of its discontinuities $\mathbb{Q} \cap [0,1]$ has Lebesgue measure zero.

Correct Answer:

$$f$ is Riemann integrable on $[0,1]$ and $\int_0^1 f(x) dx = 0$ because the set of its discontinuities $\mathbb{Q} \cap [0,1]$ has Lebesgue measure zero.

Question 5

Using the method of Lagrange multipliers, find the global maximum and minimum values of $f(x,y) = x^2 + 2y^2$ subject to the circle constraint $x^2 + y^2 = 4$.

Maximum value is 4 at $(0, \pm 2)$ and minimum value is 2 at $(\pm 2, 0)$. Maximum value is 8 at $(0, \pm 2)$ and minimum value is 4 at $(\pm 2, 0)$. Maximum value is 16 at $(\pm 2, \pm 2)$ and minimum value is 0 at $(0,0)$. Maximum value is 6 at $(\sqrt{2}, \sqrt{2})$ and minimum value is 4 at $(2,0)$.

Correct Answer:

Maximum value is 8 at $(0, \pm 2)$ and minimum value is 4 at $(\pm 2, 0)$.

Question 1

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Prepare with the ENADE Matemática Practice Questions - ENADE Matemática - Exame Nacional de Desempenho dos Estudantes Exam practice quiz. This question bank includes 100 questions covering mathbb, theorem, real, consider, and frac. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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ENADE Matemática Practice Questions - ENADE Matemática - Exame Nacional de Desempenho dos Estudantes Exam

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