tutoring for geometry and pre calculus

(1) In case (iii) D ABC is an image of itself. (2) When K = 1, we get congruent figures and congruent figures are also similar. (3) In each case, image is similar to pre-image. (4) The ratio of corresponding sides is K. (5) The corresponding sides are parallel to each other. (6) The rat..

Summary - Enlargement or Dilatation If D PQR is the image of D ABC (Pre image) and K is the enlargement factor, If K = 1 the triangles are congruent. The ratio of their areas is K 2 (SAS similarity) If a pair of corresponding angles are equal and the sides including them are proportional,..

are parallel to the sides of The point X is called the centre of enlargement. Let us consider various cases for different values of the enlargement factor. Enlargement factor greater than one. when K > 1 Let K = 2 Take O as the centre of enlargement, two possible figures are shown: (Pre..

If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..

If f (x) is a function continuous on [a, b] then Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(b) ..

The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer scienc..

After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class..

First Fundamental Theorem of Integral Calculus Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined ..

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These theorems give an..