Evaluating a Limit Consider the limit lim x → 0 + ( − x ln x ) (a) Describe the type of indeterminate form that is obtained by direct substitution. (b) Evaluate the limit. Use a graphing utility to verify the result. M FOR FURTHER INFORMATION for a geometric approach to this exercise, see the article "A Geometric Proof of lim d → 0 + ( − d ln d ) = 0 " by John H. Mathews in The College Mathematics Journal, To view this article, go to MathArticles.com.
Evaluating a Limit Consider the limit lim x → 0 + ( − x ln x ) (a) Describe the type of indeterminate form that is obtained by direct substitution. (b) Evaluate the limit. Use a graphing utility to verify the result. M FOR FURTHER INFORMATION for a geometric approach to this exercise, see the article "A Geometric Proof of lim d → 0 + ( − d ln d ) = 0 " by John H. Mathews in The College Mathematics Journal, To view this article, go to MathArticles.com.
Evaluating a Limit Consider the limit
lim
x
→
0
+
(
−
x
ln
x
)
(a) Describe the type of indeterminate form that is obtained by direct substitution.
(b) Evaluate the limit. Use a graphing utility to verify the result.
M FOR FURTHER INFORMATION for a geometric approach to this exercise, see the article "A Geometric Proof of
lim
d
→
0
+
(
−
d
ln
d
)
=
0
"
by John H. Mathews in The CollegeMathematics Journal, To view this article, go to MathArticles.com.
Compute and write a sentence explaining how you computed the limits. (seen in attached image)
(Question pertaining to indeterminate limits)
It is not uncommon for people to write:
lim x approaches a f(x) = 0/0
a) Why is this not correct?
b) Is 0/0 a number? No. Explain what 0/0 means in terms of the numerator and the denominator.
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