1

Find the angle between A = (2, 0, - 2) and B = (0, 3, - 3). First, find the scalar product.

A) 50°

B) 60°

C) 55°

D) 65°

2

Determine the values of the local extrema for each of the functions is f(x) = \$ 4x^5 - 12x^3 + x^2 - 2 \$.

A) x = 1

B) x = 2

C) x = 0

D) x = 3

3

Solve the equation \$(x^2 - 6x - 7) / (x^2 - 10x + 21)\$.

A) \$(x + 1)/(x - 3)\$

B) x = -2

C) x = 2

D) x = 1

4

Determine if the function \$f(x) = (x^2 - 1)/(x - 1)\$ is continuous at x = 1.

A) f(1) = 8

B) f(1) = 3

C) f(1) = 4

D) f(1) = 2

5

The number of real roots of the equation \$ x | x | - 5 | x + 2 | + 6 = 0 \$, is.

A) 3

B) 5

C) 4

D) 6

6

Let S = { x ∈ R : \$(\sqrt3 + \sqrt2)^x + (\sqrt3 - \sqrt2)^x\$ = 10}. Then the number of elements in S is.

A) 1

B) 0

C) 4

D) 2

7

Factor \$128x^7 - 1\$.

A) \$(2x - 3)(64x^7 + 31x^5 + 6x^4 + 18x^3 + 14x^2 + 2x + 21)\$

B) \$(2x - 1)(64x^6 + 32x^5 + 16x^4 + 8x^3 + 4x^2 + 2x + 1)\$

C) \$(x - 1)(61x^6 + 30x^5 + 26x^4 + 38x^3 + 44x^2 + 2x + 71)\$

D) \$(x - 1)(50x^6 + 21x^5 + 16x^4 + 8x^3 + 4x^2 + 55x + 12)\$

8

Solve the equation: \$ 2x^2 + 5x + 3/(x+2) \$ = 0

A) \$x = -1\$ and \$x = -(3/2)\$

B) \$x = 5/2\$ and \$x = -(3/2)\$

C) \$x = 9\$ and \$x = -(3/2)\$

D) \$x = -1\$ and \$x = -(7/2)\$

9

Evaluate the limit: \$lim_x->∞ (1- 3x + 6x^2 - x^10)/(2 + 4x^4 - 8x^7 + 8x^10)\$.

A) \$1/8\$

B) \$-2/9\$

C) \$-3/8\$

D) \$-1/8\$

10

Use synthetic division to divide \$6x^4 + x^3 - 39x^2 + 6x + 40\$ by 3x - 4.

A) (x +1) (2x -5)

B) (2x -1)(x -5) (2x +5)

C) (x +1)(x -2) (2x +5)

D) (x -1)(2x -2)(2x -5)