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Comparison Test or Limit Comparison Test In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series. When the inte
Q. Negative Signs in Fractions? It really doesn't matter where you put a negative sign in a fraction. The following are all the same: The negative sign can go in
Evaluate given integrals. ∫3/(5 y + 4) dy Solution Let's notice as well that if we take the denominator & differentiate it we get only a constant and th
Properties of Integration
The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There
Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b
Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several
Divides a given line-segment externally in the ratio of 1:2 Construction: i )Draw BX making an actueangle at B. ii) Starting from B, mark 2 equal points on BX as shown in the f
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
a) Specify that a tree has at least 2 vertices of degree 1. b) What is the largest number of vertices in a graph with 35 edges if all vertices are
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