BCA DCA1105 FUNDAMENTALS OF MATHEMATICS

Description

 

 

 

STUDENT NAME

ROLL NUMBER

BACHELOR OF COMPUTER APPLICATIONS (BCA)

SEMESTER I

SESSION: JANUARY FEBRUARY 2026

COURSE CODE & NAME: DCA1105 FUNDAMENTALS OF MATHEMATICS

 

 

 

 

 

 

 

 

 

 

 

Assignment Set – 1

 

 

Ans 1.

A limit describes the value an application reaches when its input gets closer to a particular point. In the event that direct substitution of the limit value into the expression produces the form of an unknown or undefined We are unable to find the limit with a simple substitution. It is necessary to transform the expression into a form that can be analyzed. Two of the most commonly used indeterminate expressions are zero divided by zero and infinity minus infinity. Both need algebraic manipulation or the application to a rule of thumb before evaluation can be made.

The L’Hopital’s rule is among the most effective methods for solving indeterminate form. It states that,

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Ans 2.

An important theorem in differential calculus is the Rolle Theorem. It relates the values of a function at the ends of an interval to the value of its derivative somewhere in the interval. First suggested by the French mathematician Michel Rolle, and then carefully proven with the completeness of the real numbers. Under three special conditions the theorem can be used. The first condition is that the function should be continuous on an open interval. This means it has no gaps, jumps or breaks over the interval including the end points. The second requirement is that the function be distinct on the inside of that interval that is, a well-defined line of tangent exists at every inner point. Thirdly, the function needs to

 

Ans 3.

Trigonometry has to do with the relationships between the angles and sides of triangles, with some important applications such as sine and cosine, that play a central role in physics, mathematics, and engineering. Some angles such as 0°, 30°, 45°, 60° and 90° have their trigonometric values given directly in tables or found on the unit circle but these are not the only angles that can be used. A good way to do this is to give the required angle as a product or difference of two normal angles for which the trigonometric

 

Assignment Set – 2

 

 

Ans 4.

Partial fraction decomposition is a method of algebra that permits complicated rational expressions, in other words, a part in which both the numerator as well as the denominator are polynomials, to be broken down into smaller fractions. This is especially important because it turns expressions that are difficult to work with into simpler components that are far easier to integrate, differentiate or understand. The method has widespread applications for calculus, notably with regard to the combination of rational functions and in engineering fields such as control

 

 

Ans 5.

Differentiation refers to the procedure of discovering the pace of change in a function with respect to the variable it is based on. It’s one of the two fundamental operations of calculus. The other is the integration. When a new function is constructed when two basic functions are combined by multiplication, a particular distinction rule, known as the Product Rule must be applied. The rule says that the derivative of a product of two functions is the one function

Ans 6.

Optimization is one of the most effective applications of differential calculus. It involves finding the maximum or minimum value of a value that is dependent on one or more variables, subject to certain limitations. In the context of real-world situations it is common to want to increase something that is beneficial, such as profit, area, or efficiency, or cut down on something cost-intensive like the use of materials, time or distance. Calculus’s approach is to first express the