Differentiation from First Principles is a formal method for determining a tangent's gradient.
<h3>What is meant by differentiation?</h3>
Finding a function's derivative is the process of differentiation. It is also the process of determining how quickly a function changes in relation to its variables.
According to the Sum rule, a sum of functions' derivatives equals the sum of those functions' derivatives. The derivative of two different functions is the difference of their derivatives, according to the Difference rule.
Differentiation from First Principles is a formal method for determining a tangent's gradient. The straight line connecting any two locations on the curve that are fairly near to one another will have a gradient that is similar to that of the tangent at those places.
s(t) = ∫vdt = ∫sin(πt)dt = (-cos(πt))/π + c
substituting the values t = 3, we get
s(-3) = (-cos(-3π))/π + c = 0
simplifying the above equation, we get
(-cos(3π))/π + c = 0
1/π + c = c
c = -1/π
Therefore, the correct answer is s(t) = (-cos(πt))/π - 1/π = (-cos(πt) - 1)/π.
The complete question is:
Given the velocity v=ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v=sin(pi*t), s(-3)=0
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