Mathematics - 2013 E.C (2020/2021) Ethiopian University Entrance Exam (EUEE)

A $\left\{ n \sin\left(\frac{1}{n}\right) \right\}$

B $\left\{1-\frac{1}{n}\right\}$

C $\left\{\ \frac{n}{n+1}\right\}$

D $\left\{\ \cos\frac{n}{n}\right\}$

A $$\lim_{n \to \infty} (3a_{n} + 2b_{n}) = 3L + 2M$$

B $$\lim_{n \to \infty} (a_{n} - b_{n}) = L - M$$

C $$\lim_{n \to \infty} \left( \frac{a_{n}}{b_{n}} \right) = \frac{L}{M}$$

D $$\lim_{n \to \infty} a_{n} b_{n} = LM$$

A -1

B -3

C 1

D 0

A The continuity of the function at P.

B The slope of a secant line through P.

C The slope of the tangent line through P.

D The graph of f has no jump at P.

A -1

B -3

C 3

D 1

A $4f(x)$ and $2nf(x)$

B $2f(x)$ and $nf(x)$

C $9f(x)$ and $3nf(x)$

D $9f(x)$ and $n^2f(x)$

A It is the y-intercept of the function.

B It is the x-intercept of the function.

C It is the concavity point of the function.

D It is the critical point of the function.

A Its critical numbers are 0 and 2 and its maximum value is 15.

B Its critical numbers are 0, 2, 3 and its maximum value is 0.

C It has critical numbers at 0 and 2 and its maximum value is 0.

D Its critical numbers are 0 and 2 and its maximum value is -4.

A 1

B $-\frac{3}{2}$

C 2

D $\frac{3}{2}$

A L = 2,500 m and W = 2,000 m

B L = 2,500 m and W = 2,500 m

C L = 5,000 m and W = 5,000 m.

D L = 3,000 m and W = 2,500 m.