MTH107 Calculus I SUSS Assignment Sample Singapore

MTH107 Calculus I course is designed to provide a comprehensive introduction to the principles of calculus. This course will cover topics such as limits and continuity, derivatives, integrals, and their applications to problem-solving. Students will learn how to find the slope of a curve, calculate derivatives and apply them in various contexts.

They will also explore integration techniques to solve certain problems and use these methods in solving different types of equations. The course also covers topics such as parametric curves, vector calculus and partial derivatives. Through this course, students will gain a better understanding of the processes involved in calculus and its applications to other areas of mathematics. Additionally, students will learn about the history of the calculus and its development through time.

Unlock your potential in MTH107 Calculus I by discovering a vast array of assignment samples.

Singaporeassignmenthelp.com  offers the best MTH107 Calculus I assignment help to students. Our experts provide solutions with detailed explanations and well-formatted reports. Whether you are dealing with a complex calculus problem or need help with an equation, our team of professional writers can offer comprehensive assistance in all areas of calculus.

Here, we will explain various assignment briefs. These include:

Assignment Brief 1: Discuss the continuity or differentiability of certain functions of one variable.

When examining the functions of one variable, it is important to consider their continuity and differentiability. Continuity refers to the function’s ability to have a continuous graph without any gaps or jumps, while differentiability refers to its ability to have a tangent line at each point on its graph. These factors play a significant role in understanding the behavior of a function and its applicability in various fields, such as mathematics, physics, and engineering.

By analyzing and manipulating the properties of these functions, we can gain a deeper understanding of their behavior and use them to solve complex problems. Therefore, studying the continuity and differentiability of functions of one variable is crucial in the field of mathematics and its various applications.

Assignment Brief 2: Apply derivative tests to find the relative extremum of certain functions of one variable.

One of the fundamental concepts in calculus is finding the relative extremum of a function of one variable. This is an important process for analyzing a function’s behavior and optimizing it. Derivative tests are commonly used for finding the relative extrema of a function.

For example, the first derivative test checks for critical points by finding where the derivative equals zero or does not exist. The second derivative test confirms whether these critical points are local maxima or minima. Applying these tests requires a strong understanding of calculus, and can provide invaluable insights into the properties of a function. Using derivative tests to find relative extrema is an essential tool for any professional mathematician or scientist.

Assignment Brief 3: Show the existence of certain points in certain open intervals satisfying certain identities using the Intermediate Value Theorem or Mean Value Theorem.

The Intermediate Value Theorem and Mean Value Theorem provide powerful tools for proving the existence of certain points in certain open intervals satisfying various identities. With applications across calculus and other areas of mathematics, these theorems allow us to establish the existence of key values without having to show their exact form.

By leveraging the continuity and differentiability of functions developed in calculus, we can draw on these theorems to solve even challenging problems, providing insight into the behavior of these functions and revealing hidden patterns in the data. Whether you’re tackling a challenging math problem or simply seeking to broaden your understanding of these foundational principles, the Intermediate Value Theorem and Mean Value Theorem represent critical tools in your mathematical toolkit.

Assignment Brief 4: Sketch graphs of certain functions of one variable.

Sketching graphs of functions of one variable is an essential part of understanding calculus and statistics. By visually mapping out the behavior of a function, we can gain insights into its properties and relationships to other functions. Whether you are working with sine and cosine functions, logarithmic functions, or polynomial functions, drawing accurate and clear graphs are vital to making sense of complex equations.

With the help of modern graphing calculators and computer software, it is more accessible than ever to produce high-quality graphs quickly and efficiently. So, let’s not shy away from the challenge of sketching graphs and embrace the power of visualization to enhance our understanding of mathematical concepts.

Assignment Brief 5: Determine the limits of certain functions of one variable.

As mathematicians, we are constantly striving to push the boundaries of what is possible. One way we do this is by determining the limits of certain functions of one variable, which involves analyzing the behavior of these functions as their input approaches a certain value. This concept may seem abstract, but it has crucial applications in fields such as physics and engineering, where precise calculations are essential.

By understanding the limits of functions, we gain a deeper insight into how they behave and can make more accurate predictions about their behavior in the future. It is a challenging and rewarding pursuit that allows us to uncover new depths of mathematical knowledge.

Assignment Brief 6: Use the Taylor polynomial of a certain degree of a given function to estimate the value of the function at a certain point up to a certain degree of accuracy.

When faced with the task of estimating the value of a function at a certain point, the Taylor polynomial can be a valuable tool. By using a specific degree of the polynomial, we can ensure that our estimate is accurate up to that degree. This technique can be particularly useful when dealing with complex functions where it is not possible to calculate the value directly.

However, it is important to remember that the accuracy of our estimate will depend on the degree of the polynomial used. It is therefore essential to carefully consider the degree required in order to achieve the desired level of accuracy. By using the Taylor polynomial in this way, we can confidently estimate the value of a function and make informed decisions based on our calculations.