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 2 g(x) = (2x + 1)/(5x + 6) b. Express the following function graphically, and comment about the region which can't be the range from the graph. 3 f(x) = { x^2 - 1 ; x < 0 { x ; 0 ≤ x < 1 { 2/x ; x ≥ 1 c. Express the following absolute value function into a piecewise function 2 f(x) = |x - 1| + |2x + 1| + |x| 3. a. Compute the continuity of the following function at x = π/2 3 f(x) = { 1 + sin x ; x < π/2 { 2 + (x - π/2)^2 ; x ≥ π/2 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