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.
One-sided limits
a. Evaluate lim Vx - 2.
xS2+
b. Explain why lim Vx - 2 does not exist.
xS2-
xa g(x)
find the limits that exist. If the limit does not exist, explain
2. Use the graphs of f and g in the accompanying figure to
find the limits that exist. If the limit does not exist, explain
why.
(a) lim [f(x)+ g(x)]
(b) lim [f(x) + g(x)]
(c) lim [f(x)+ g(x)]
(d) lim [f(x) + g(x)]
f(x)
1+ g(x)
(e) lim
x21+g(x)
(f) lim
x2
f(x)
(g) lim Vf(x)
(h) lim Vf(x)
y = f(x)
AY
y g(x)
%3D
A Figure Ex-2
Figure out that this statement is true or false? if is false explain why? by using example, and if it is true explain why?
When lim x → a f ( x ) exists, the limit is always equal to f ( a ) - Is this statement true or false?
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