Sample Calculus Problems with Solutions
Problem 1: Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of edges of the cube.
Solution:
According to the given condition,
Let △x be the error in the length and △y be the error in the surface area
Let’s take length as x
△x/x × 100 = 1
△x = x/100
x+△x = x+(x/100)
As, surface area of the cube = 6x2
dy/dx= 6(2x) = 12x
△y = dy/dx △x
△y = (12x) (x/100)
△y = 0.12 x2
So, △y/y = 0.12 x2/6 x2 = 0.02
Percentage change in y = △y/y × 100 = 0.02 × 100 = 2
Hence, the percentage error in calculating the surface area of a cubical box is 2%
Problem 2: If x3 + y3 = 3axy, find dy/dx.
Solution:
Given, x3 + y3 = 3axy
Differentiating both sides with respect to x, we get:
3x2 + 3y2 (dy/dx) = 3ay + 3ax (dy/dx)
⇒ {3y2 – 3ax} (dy/dx) = 3ay – 3x2
⇒ dy/dx = (3ax – 3x2)/(3y2 – 3ax)
⇒ dy/dx = (ax – x2.)/(y2 – ax).
Calculus | Differential and Integral Calculus
In mathematics, Calculus deals with continuous change. It is also called infinitesimal calculus or “the calculus of infinitesimals”. The Two major concepts of calculus are Derivatives and Integrals.
- The derivative gives us the rate of change of a function. It describes the function at a particular point while the integral gives us the area under the curve.
- The integral gives us the area under the curve. Integral gathers the different values of a function over a number of values.
In general, classical calculus Calculus is the study of the continuous change of functions. In this article, we have provided everything related to Math Calculus for Beginners. Definition, examples, and practice questions will help you not only learn calculus theory but also practice calculus.
Table of Content
- What is Calculus?
- Basic Calculus
- Calculus Topics
- Calculus Functions
- Types of Calculus
- Differential Calculus
- Integral Calculus
- Calculus Formulas
- Advanced Calculus
- Applications of Calculus
- Sample Calculus Problems with Solutions
- Practice Questions on Calculus
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