Basic Mathematics

• Chapter 1: Functions and Their Properties. Notes and past questions on Functions and Their Properties for TU BIT Basic Mathematics.
• Chapter 2: Limits and Continuity. Notes and past questions on Limits and Continuity for TU BIT Basic Mathematics.
• Chapter 3: Asymptotes and Curve Behavior. Notes and past questions on Asymptotes and Curve Behavior for TU BIT Basic Mathematics.
• Chapter 4: Derivatives and Differentiation. Notes and past questions on Derivatives and Differentiation for TU BIT Basic Mathematics.
• Chapter 5: Applications of Derivatives. Notes and past questions on Applications of Derivatives for TU BIT Basic Mathematics.
• Chapter 6: Integration and Antiderivatives. Notes and past questions on Integration and Antiderivatives for TU BIT Basic Mathematics.
• Chapter 7: Applications of Integration. Notes and past questions on Applications of Integration for TU BIT Basic Mathematics.
• Chapter 8: Series and Sequences. Notes and past questions on Series and Sequences for TU BIT Basic Mathematics.
• Chapter 9: Multivariable Calculus. Notes and past questions on Multivariable Calculus for TU BIT Basic Mathematics.
• Chapter 10: Differential Equations. Notes and past questions on Differential Equations for TU BIT Basic Mathematics.

• Explanation of Limits and Function Analysis (2081)
• Find the derivative of $y = \frac{\tan^{-1} x}{\sqrt{x}}$ with respect to $x$. Find the area of the region bounded by $y = -x$ and $x = y... (2081)
• Question What is initial value problem? Find the solution of the initial value problem $x\frac{dy}{dx} - y = x^2$, $y(2) = 5$. Evaluate:... (2081)
• Evaluate: $$\int \sqrt{4 - x^2} \, dx$$ [5] (2081)
• Find the volume of the solid obtained by rotating about the y-axis the region bounded by $y = x$ and $y = x^2$. [5] (2081)
• Evaluate: $$\int_0^5 \frac{dx}{\sqrt{x - 2}}$$, if it exists. [5] (2081)
• Test whether the series $\sum_{n=2}^{\infty} \frac{2}{n^2 - 1}$ converges or diverges. [5] (2081)
• Use Newton's method to find $\sqrt[4]{10}$ correct to four decimal places. [5] (2081)
• Find the partial derivatives $f_x$, $f_y$ and $f_{xy}$ of $f(x,y) = \sqrt{x} y^3 + x^4 y$ at $(-4,1)$. [5] (2081)
• Verify mean value theorem for the function $f(x) = x^2 + 3x + 1$ in $[-1,1]$. [5] (2081)
• Test whether the function $f(x) = \begin{cases} \dfrac{x^2 - 2x}{x - 2}, & x \ne 2 \\ 1, & x = 2 \end{cases}$ is continuous or discontinu... (2081)
• Evaluate: $$\int_0^{\pi} x \sin x \, dx$$ [5] (2081)
• (question text pending review) # Solution ## Part 1: Gradient and Directional Derivative [5 marks] **Definition of Gradient:** The gradie... (2080)
• Evaluate $\int_{0}^{\frac{\pi}{4}} \frac{dx}{1-\sin x}$, Evaluate $\int x^2 \sin x \, dx$. Solve the differential equation $\frac{dy}{dx}... (2080)
• State Rolle's Theorem and show that $x^3 + 3x + 1 = 0$ has exactly one real solution. Find the area of the region enclosed by the parabol... (2080)

Frequently asked questions

Based on the official syllabus.