Genesismath Solutions platform
admin Use the Theorem of Pythagoras to find the length of the line segment from to , and confirm that the value is consistent with the length computed using (a) Formula (4) (b) Formula (5). Solution: Given points are and . (a) Formula (4) is given by Equation of the line … Read more
1-4 use cylindrical shells to find the volume of the solid generated when the shaded region is revolved about the indicated axis. (1) (2) solving and simultaneously (3) (4) Solving … Read more
Find the volume of the solid that results when the shaded region is revolved about the indicated axis. (1) (2) (3) Solving for (4) Solving for when , then : (5) … Read more
1-4. Find the area of the shaded region. (1) The curve lies above the curve and the shaded region is bounded from left side at and from the right side by the line . (2) The curve lies above the curve . The two curves intersects at ( the shaded region bounded … Read more
Question 1. Evaluate. (a) (b) (c) (d) (e) (f) Question 2. (a) (b) (c) (d) (e) (f) Questions 3-8. Write each expression in sigma notation but do … Read more
EXERCISE Evaluate the integrals using appropriate Substitutions then the above integral becomes From (1) substituting into (2). then the integral (1) becomes Now substituting into (3) Then the above integral becomes Substituting into (1) … Read more
In this section, we shall develop the concept of antiderivatives. It contains solutions to integration problems. (1) — In each part, confirm that the formula is correct…. (a) corresponding integration formula: (b) Corresponding integration formula: (2)—In each part, confirm that the stated formula is correct by differentiating. … Read more
Exercise 4.5 Question 1 Let be the required number, then the reciprocal is . differentiating (1) w.r.t Set But only lie in the interval , therefore neglecting . Now substituting , and in (1) (a) is as small … Read more
Exercise 4.4 Question 7 Find the absolute maximum and minimum values Solution Since it is a polynomial, therefore its continuous and differentiable everywhere. To find critical points: differentiating w.r.t Set The critical point lies in the interval .Therefore the absolute maximum and absolute minimum must occur … Read more
EXERCISE 4.1 10. (a) is increasing on (b) is not decreasing anywhere. (C) is concave up on and (d) is concave down (e) the -coordinates of all inflection points and 15-32. Find (a) the intervals on which is increasing, (b) open intervals on which is decreasing (c) the open intervals on which is concave … Read more