Exam Questions

Part I: True or False

• Question 1: $lim_{x \to 3^+} \sqrt{3-x} = 0$ is presented as TRUE/FALSE (1 pt).
• Question 2: If $f$ is a polynomial function, then $lim_{x \to m} f(x) = f(m)$. (1 pt)
• Question 3: The horizontal line $y = L$ is a horizontal asymptote to the graph of $f$ if and only if $lim_{x \to \infty} f(x) = L$. (1 pt)
• Question 4: Two matrices are equal if they have the same size and corresponding entries are identical. (1 pt)
• Question 5: For any square matrix $A$, $A$ is skew-symmetric if and only if $A = A^t$. (1 pt)
• Question 6: The determinant of a matrix and its transpose are equal. (1 pt)

Part II: Fill in the Blanks

• Question 1: Given $f(x) = \begin{cases} \frac{2x^2 - 5x - 3}{x-3}, & x \neq 3 \ 4k, & x = 3 \end{cases}$ and $f$ is continuous at $x = 3$, find the value of $k$. (2 pts)
• Question 2: The value of $lim_{x \to 1^-} \frac{ln(x)}{x-1}$ is (2 pts).
• Question 3: If $A$ is an invertible square matrix and $det(A) = 5$, then find:
  • a) $det(A^T) =$
  • b) $det(A^{-1}) =$
• Question 4: If $A = [-3]$, then $|-3| =$. (2 pts)
• Question 5: If $A$ is a square matrix of order 3 and $det(A) = 2$, then $det(3A) =$. (2 pts)
• Question 6: Let $A = \begin{bmatrix} sine & cose \ cose & sine \end{bmatrix}$, then $|A| =$. (2 pts)