# Category Archives: School Learning

Evaluate the following limits in Exercises 1 to 22. Question 1:  Solution: In , as x⇢3  Put x = 3, we get  = 3+3  = 6… Read More
Evaluate the following integrals. Question 1. ∫(x2 + 1)/(x4 + x2 + 1)dx Solution: We have, ∫(x2 + 1)/(x4 + x2 + 1)dx = ∫x2(1… Read More
Question 1. Differentiate the following functions from first principles e-x Solution: We have, Let, f(x)=e-x f(x+h)=e-(x+h) =-e-x Question 2. Differentiate the following functions from first… Read More
Question 1. A soft drink is available in two packs: (i) a tin can with a rectangular base of length 5 cm and width 4… Read More
Question 1. In each of the following systems of equation determine whether the system has a unique solution, no solution, or infinite solutions. In case… Read More
Question 1.  Solution: Given, By Applying limits, we get, ⇒ =    (Indeterminate form or 0/0 form) So, we cannot just directly apply the limits as we… Read More
Question 17: Solution: In, as x⇢0 As we know, cos 2θ = 1-2sin2θ Substituting the values, we get = Put x = 0, we get… Read More
Question 49. Find the sum of first n odd natural numbers. Solution: First odd natural numbers are 1, 3, 5, 7, . . .2n –… Read More
Question 1. In a triangle OAB, if P, Q are points of trisection of AB, Prove that OP2  + OQ2 = 5/9 AB2. Solution: Given… Read More
Question 1. Find the maximum and minimum values, if any, of the following function given by (i) f(x) = (2x – 1)2 + 3  … Read More
Question 1. ∫1/[(x − 1)√(x + 2)]dx Solution: We have, ∫1/[(x − 1)√(x + 2)]dx Let x + 2 = t2, so we get, xdx… Read More
Question 11. Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A… Read More
Question 17. The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular faces is… Read More
Question 1. (i) In fig., if AB || CD, find the value of x. Solution: Given,   AB∥ CD. To find the value of x. Now,… Read More
Question 1: Insert 6 geometric means between 27 and 1/81. Solution: Let the six geometric means be A1, A2, A3, A4, A5, A6. Now, these… Read More