Additional chapter for evaluation indeterminate limits of functions and series in teaching mathematics for engineering education

Abstract

Infinity divided by infinity, zero divided by zero, one divided by zero are the most important indeterminate forms obtained when  evaluating limits for single variable functions and series. Well-known method; L' Hôpital rule has been employed to simplify and resolve  these indeterminate forms' limits such that 0/0, ∞/∞ , 1/0 in terms of quotients of their derivatives. In some cases, L' Hôpital rule is  applied more than once to solve indeterminate limits. Besides, it is so complicated to take the derivative for some functions of a single  variable and series, so L' Hôpital rule is ineffective and not practical to solve limits with indeterminate forms for those functions and  series. L' Hôpital rule is also impractical for the indeterminate limits in the form: - ∞∙0By considering all these facts, new approaches  including Central Finite Difference (CFD), Forward Finite Difference (FFD), Backward Finite Difference (BFD), High Accurate Central Finite  Difference (HACFD), High Accurate Forward Finite Difference (HAFFD), High Accurate Backward Finite Difference (HABFD) methods are  presented that provides efficient ways to solve these limits. Taking derivative is not required in all approaches. HACFD with step size:  0.0001 is the most preferred technique here to obtain exact results among all other techniques.