Explain in your own words Assignment Example | Topics and Well Written Essays - 500 words

Explain in your own words - Assignment Example Note that, the indefinite integrals of a function only differ by a constant (Dawkins 2014). Intuitively, this second part, opens the first part of the theorem to include the entire interval, not limited by (a,b).It holds that if F (x)and f(x) are functions such that , F(x) is an integral of f(x), then F’(x) = f(x) Assuming that a,is constant, then f (a) is zero, and if f(x) is x, then g’(x) =1, hence the whole term becomes f (g(x). Therefore, the definite integral is only influenced by the derivative, with the constant in the indefinite integral being a dummy. L’Hospital’s rule is a principle that helps to determine the limits of indeterminate forms. There are two most common indeterminate forms I.e. 0/0 and ∞/-∞ in which L’hospital rule majorly occurs. Note that these indeterminate forms create a controversy in the expected results. For instance, if we divide zero by zero, the answer may be 1(any number divided by itself is one), ∞ (any number divided by 0 = ∞) or 0 (zero divided by any number is zero) and so does the second case. therefore, there is need to manipulate indeterminate functions in order to obtain limits. Secondly, factoring out functions could be so tedious, and since derivatives reduce the highest power, then L’hospital rule can also be used (Ikenaga, 2005). L’hospital rule states that; Note that as x approaches infinity then the numerator also approaches infinity while the denominator approaches negative infinity, and thus (∞/-∞), moreover, if we x takes the value 2, then the function becomes (0/0), both of which are indeterminate forms. The Taylor series is an expression of a given function as the summation of infinite term obtained from its derivatives about a point. The effectiveness of Taylors function in approximating the function is based on the fact that, it sums up all the