cj5892 said:Homework Statement
Consider the infinite series s(x)=1-tan^2(x)+tan^4(x)-tan^6(x)+... , where 0<x<pi/4
s'(x)=
A.sin2x
B.cos2x
C.-tan2x
D.-sin2x
E.-cos2xThe Attempt at a Solution
Attempting to derive the series, i get 1-2tanxsec^2x+4tan^3(x)sec^2(x)-6tan^5(x)sec^2(x)+...
am i missing something obvious here? i don't see any trig identities in that that would give any of the answers
cj5892 said:i still can't get it :(
The derivative of an infinite series is the mathematical concept that represents the rate of change of the series at a particular point. It is calculated by taking the limit of the difference quotient of the series as the change in the independent variable approaches zero.
The derivative of an infinite series can be calculated using various methods such as the power rule, product rule, quotient rule, or chain rule. These rules are applied to each term in the series and the resulting terms are summed together to get the derivative of the entire series.
The derivative of an infinite series represents the slope of the tangent line to the graph of the series at a certain point. This means that the derivative gives us information about the rate of change of the series and can help us analyze the behavior of the series at different points.
The derivative of an infinite series has many practical applications in fields such as physics, engineering, economics, and finance. It is used to calculate rates of change, optimize functions, and model complex systems. For example, the derivative of a power series can be used to analyze the behavior of electrical circuits or the growth of populations.
No, the derivative of an infinite series cannot always be calculated. In some cases, the series may not be differentiable at certain points or the derivative may not exist. Additionally, some series may be too complex to find an exact derivative and can only be approximated using numerical methods.