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.
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
4. Use cylindrical shells to find the volume of the solid generated when the
region enclosed by the given curves is revolved about the x-axis.
y = √√x, y = 0, y = √√3
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