Mathematics I

Daffodil International University Faculty of Science & Information Technology Department of Software Engineering Midterm Examination, Fall 2026 Course Code: MAT101; Course Title: Mathematics I Batch: 48; Section: A-O; Teachers Initial: MMH, ZT, MSIM, NDP, MMK Time: 1 Hour 30 Minutes Marks: 25 Answer ALL Questions [The figures in the right margin indicate the full marks and corresponding course outcomes. All portions of each question must be answered sequentially] 1. Explain the followings: a. Bijective Function, it's condition with a suitable example. [1] b. Geometrical meaning of differentiation. [1] c. The concept of limits for a real-valued function f(x). [1] 2. a. Compute the domain and range of the following function g(x) = (2x + 1) / (5x + 6) [2] b. Express the following function graphically, and comment about the region which can't be the range from the graph. f(x) = { x^2 - 1 ; x < 0 x ; 0 ≤ x < 1 2/x ; x ≥ 1 [3] c. Express the following absolute value function into a piecewise function f(x) = |x - 1| + |2x + 1| + |x| [2] 3. a. Compute the continuity of the following function at x = π/2, f(x) = { 1 + sin x ; x < π/2 2 + (x - π/2)^2 ; x ≥ π/2 [3] b. Compute dy/dx for (cos x)^y = (sin y)^x [3] c. Compute dy/dx for y = x^x + (sin x)^(ln sqrt(x)) [3] d. Compute the derivative of x^(ln sqrt(a^(cos^-1 x))) + a^(2^x) with respect to cot^-1 (x / sqrt(1 - x^2)) [3] e. If y = (ax + b)^n then calculate y_n, y_s, and y_p where, s < n and p > n. [3]