University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2021
Views:

355

Pages:

4
Author:

Clint W.

1 INDEТERMINANT FORMS AND L'HOPITAL'S RULE ASSIGNMENT 1 1 Objectives: 1 1 • • 1 1 Recognize limits that produce indeterminate forms. 1 1 Apply l'Hopital's Rule to evaluate а lirnit . lndeterminate Forms >тhе forms 0/0 and 00/00 are called indeterminate because they do not guarantee that а limit exists, nor do they indicate what the limit is, if one does exist. When you encountered one of these indeterminate forms earlier in the text, you attempted to rewrite the expression Ьу using various algebraic techniques. /ndetenninate Form о о 00 00 Algebraic Technique Umil 2..х2 - 2 lim --.r➔-1 x+l з.� - I lim --.r➔oo 2.\.J + 1 lim 2(х = .r➔-1 1) Divide numerator and (х + l ). denominator Ьу 1 = -4 2 ) з --(1/х = 1.1m �"'" х➔оо 2 + () /х 2) 3 =- 1 Divide numerator алd denominator Ьу х2• 1 1 1 1 2 1 1 1 Occasionally, you сап extend these algebraic techniques to find limits of transcendental functions. For instance, the limit - 1 ' e2rJ,m.r-+o е Х - \ produces the indeterminate form 0/0. Factoring and then dividing produces 1 1 1 1 1 = lim (e-t + 1) 1 Х ➔О 1 1 = 2. 1 1 1 Not all indeterminate forms, however, can Ье evaluated Ьу algebraic manipulation. This is often true when both algebraic and transcendental functions are involved. For instance, the limit 1 1 1 е2х _ 1 li111--- x-to 1 Х 1 1 produces the indeterminate form 0/0. Rewriting the expression to obtain 1 1 1 . (е21• 1 1) 1 1 11111 --- .t-tO Х 1 Х 1 1 1 merely produces another indeterminate form, оо - оо. 1 1 1 1 1 1 1