In order to determine a limit from a graph: Both green arrows must point to the same number and Both arrows must be on the function’s line. Both arrows are not on the function’s line, so the limit does not exist. Example question 3: What is the limit as x approaches 1?
To find the power series for ln(1 - x) we will: Derive the power series for a related function: 1 / (1 - x) Integrate to find the power series for ln(1 - x) Determine the interval of convergence Step 1: Use long division to find the power series for 1 / (1 - x) ...
Definite integrals are a type of integral wherein the integration is done within a defined interval. The interval can be either open or closed, as long as one is present. Unlike indefinite integrals, where the answers are functions, the answers to definite integrals have actual values. The int...
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{eq}\bullet {/eq}Power, the logarithm of a variable to the {eq}k {/eq}th exponent equals, {eq}\log_a x^k=k\log_a x {/eq}. Answer and Explanation:1 Let us solve the integral, {eq}I=\displaystyle \int \cot x \, dx {/eq}. ...
First of all, we should calculate the indefinite integrals: I k ( r ) = ∫ d r r 2 R k 2 ( r ) = n k 3 8 ∫ d q q k 2 Q k 2 ( q k ) (113) where integration variable r is transformed into dimensionless ones, q k = 2 Z k r n k r B (114) At k = 1...
First of all, we should calculate the indefinite integrals: I k ( r ) = ∫ d r r 2 R k 2 ( r ) = n k 3 8 ∫ d q q k 2 Q k 2 ( q k ) (113) where integration variable r is transformed into dimensionless ones, q k = 2 Z k r n k r B (114) At k = 1...
First of all, we should calculate the indefinite integrals: I k ( r ) = ∫ d r r 2 R k 2 ( r ) = n k 3 8 ∫ d q q k 2 Q k 2 ( q k ) (113) where integration variable r is transformed into dimensionless ones, q k = 2 Z k r n k r B (114) At k = 1...