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Differential calculus by das and mukherjee pdf downloadgolkes The differential calculus is a branch of mathematics which studies the rates at which quantities change. Differential calculus is used in physics, chemistry, fluid dynamics, classical mechanics and statistics. Typically, differential calculus involves finding the tangent line to a curve or differentiating two functions like y=f(x) and y=g(x). The next section below gives instructions for what to do when you want to find the tangent line for a given function at a given point on the x-axis. Finding the tangent line for a function at a point. $ $ $ $ $ $ $ The given curve is smooth and so we can find its derivative as follows: We see that the tangent line does not pass through the point (1,1). The graph of this function has at most one point on the x-axis where the derivative is not $0$, and it is at (0,0). The graph of y=f(x) + k(x) has a vertical asymptote of f(x). If we differentiate this twice we get: More on calculus at Khan Academy: http://www.khanacademy. org/math/calculate-derivatives-using-integrals If we integrate the given function to find its value at a particular point on the x-axis we get: Note that if we try to evaluate the integral of y=k. at -2,0, we get a negative value of −1. Differentiating this with respect to x shows that the derivative is indeed −1. Instead of trying to evaluate this integral as −1, let's just plug in an arbitrary number instead. We now have: ∫ −2,0 e x(−2)dy = 1. Note that the 1 in the integrand has disappeared! We have found a point at which y = −k(x) is tangent to the curve. This point is 1. Our value for x is (−2). Differentiating this function twice with respect to x yields: The graph of y=f(x) + k(x) also has at most one point on the x-axis where f(x) is not equal to 0, so it must be at (0,0). To find the function's derivative at this point, let's start by using f'(0) = f'(−2)=4. You may notice that f'(0) is the y-coordinate of the point (−2,4), which is one of the points given above on the graph. We get: Notice that when we plug in a number for x, we get a number in return! If we plug in a number for x with a plus sign, we get positive numbers in return. If we plug in a number for x with a minus sign, we get negative numbers in return. Also note that if we plug in zero for x, then all of these functions are equal to zero. 40cfa1e7782066
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