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

Explain in your own words - Assignment ExampleNote that, the indefinite integrals of a function however 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(prenominal) 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 that influenced by the derivative, with the constant in the indefinite integral being a dummy.LHospitals rule is a principle that helps to determine the limits of enigmatic forms. There are two most common indeterminate forms I.e. 0/0 and /- in which Lhospital 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 change integrity 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 Lhospital rule can also be utilize (Ikenaga, 2005). Lhospital rule states thatNote 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 assess 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 virtually a point. The effectiveness of Taylors function in approximating the function is based on the fact that, it sums up all the