Mathematics I

• Chapter 1: Function of One Variable. Notes and past questions on Function of One Variable for TU BSc CSIT Mathematics I.
• Chapter 2: Limits and Continuity. Notes and past questions on Limits and Continuity for TU BSc CSIT Mathematics I.
• Chapter 3: Derivatives. Notes and past questions on Derivatives for TU BSc CSIT Mathematics I.
• Chapter 4: Applications of Derivatives. Notes and past questions on Applications of Derivatives for TU BSc CSIT Mathematics I.
• Chapter 5: Antiderivatives. Notes and past questions on Antiderivatives for TU BSc CSIT Mathematics I.
• Chapter 6: Applications of Antiderivatives. Notes and past questions on Applications of Antiderivatives for TU BSc CSIT Mathematics I.
• Chapter 7: Ordinary Differential Equations. Notes and past questions on Ordinary Differential Equations for TU BSc CSIT Mathematics I.
• Chapter 8: Infinite Sequence and Series. Notes and past questions on Infinite Sequence and Series for TU BSc CSIT Mathematics I.
• Chapter 9: Plane and Space Vectors. Notes and past questions on Plane and Space Vectors for TU BSc CSIT Mathematics I.
• Chapter 10: Partial Derivatives and Multiple Integrals. Notes and past questions on Partial Derivatives and Multiple Integrals for TU BSc CSIT Mathematics I.

• Sketch the graph of $f(x) = x^2$. Find its domain and range. Evaluate $\lim_{x \to 1^-} \sin^{-1} \left( \frac{1-\sqrt{x}}{1-x} \right)$... (2081)
• Where the function $f(x) = |x|$ is differentiable? Discuss. A farmer has 1200 m. of fencing and wants to fence off a rectangular field th... (2081)
• Find the solution of the initial value problem $x^2 y' + x y = 1$, $y(1) = 2$, $x > 0$. Find the area enclosed by the line $y = x - 1$ an... (2081)
• Evaluate $\int_0^3 \sqrt{1 + x^2} \cdot x^3 \, dx$ [5] (2081)
• Find the Maclaurin series expansion of $f(x) = \sin x$ for all x. [5] (2081)
• Find the unit normal and binormal vectors for the circular helix $\mathbf{r}(t) = \cos t \hat{i} + \sin t \hat{j} + t \hat{k}$. [5] (2081)
• If $f(x,y) = \frac{xy}{x^2 + y^2}$, does $\lim_{(x, y) \to (0, 0)} f(x, y)$ exist? Justify. [5] (2081)
• Determine whether the sequence $a_n = (-1)^n$ is convergent or divergent. [5] (2081)
• The position vector of an object moving in a plane is given by $\mathbf{r}(t) = t^2 \hat{i} + t^2 \hat{j}$. Find its velocity, speed, and... (2081)
• Show that every member of the family of function $y = \frac{1 + ce^t}{1 - ce^t}$ is a solution of the differential equation $y' = \frac{1... (2081)
• If $f(x,y) = 2x^3 + x^2y^2 - y^4$, find $f_x(1,-2)$, $f_y(1,-1)$ and $f_{yx}(1,-1)$. [5] (2081)
• Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under the curve $y = \sqrt{x}$ fo... (2081)
• If $\vec{a}=(4,0,3)$ and $\vec{b}=(-2,1,5)$, find $|\vec{a}|$, $3\vec{b}$, $\vec{a}+\vec{b}$ and $2\vec{a}+5\vec{b}$. Estimate the value... (2080)
• As dry air moves upward, it expands and cools. If the ground temperature is $20°C$ and the temperature at height of 1 km is $10°C$, expre... (2080)
• The area of the parabola $y = x^2$ from (1,1) to (2,4) is rotated about the y-axis. Find the area of the resulting surface. Find the solu... (2080)

Frequently asked questions

Based on the official syllabus.