This question aims to learn the basic methodology for optimizing a mathematical function (maximizing or minimizing). Critical points are the points where the value of a function is either maximum or minimum. To calculate the critical point(s), we equate the first derivative’s value to 0 and solve for the independent variable. We can use the […]

# Category Archives: Pre Calculus Q&A

The main objective of this question is to check whether the addition of the given two functions when both the functions are odd, even or one is odd and the other is even results in even or odd function. This question shows the concept of even and odd functions. An even function is mathematically represented as: [f(-x) […]

( x + 3 ) y” + x y’ + ( ln|x| ) y = 0, y(1) = 0, y'(1) = 1 The aim of this question is to qualitatively find the possible interval of the differential equation’s solution. For this we need to convert any given differential […]

f(x,y) = 1 + x ln (xy – 5), (2,3) This problem explains why the given function is differentiable at a point, and to find the linearization at that point. The concept required to solve […]

This question aims to find the total area enclosed by a wire when it is cut down into two pieces. This question uses the concept of the area of a rectangle and an equilateral triangle. The area of a triangle is mathematically equal to: [Area space of space triangle space = space frac{Base space times space […]

(dfrac{4}{x+5}+dfrac{2}{x-5}=dfrac{32}{x^2-25}) This question aims to find the solution to the given equation by taking into consideration the restrictions on the given function. The fraction of two polynomials is said to be a rational expression. Such expression can be expressed as $dfrac{a}{b}$ in which $a$ and $b$ both are polynomials. The product, sum, division, and subtraction […]

When he is $10$ feet from the base of the light, at what rate is the tip of his shadow moving? When he is $10$ feet from the base of the light, at what rate is the length of his shadow changing? The purpose of this question is to find the rate of change of […]

(a=begin{bmatrix}3\-4end{bmatrix}, b=begin{bmatrix}-7\8end{bmatrix}) This question aims to find the parametric equation of the line through two given vectors. A parametric equation is an equation that incorporates a parameter that is an independent variable. In this equation, the dependent variables are the continuous functions of the parameter. Two or more parameters can also be used if needed. […]