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Mathematics
Mathematics
Problem
Evaluate the following limits. Show all necessary steps and clearly indicate the final answers. a. (i)
lim
x
→
1
(
e
x
2
+
3
x
−
5
)
\displaystyle \lim_{x \to 1} \bigl(e^{x^{2}}+3x-5\bigr)
x
→
1
lim
(
e
x
2
+
3
x
−
5
)
b. (ii)
lim
x
→
0
(
ln
(
1
+
x
)
+
2
x
)
\displaystyle \lim_{x \to 0} \bigl(\ln(1+x)+2x\bigr)
x
→
0
lim
(
ln
(
1
+
x
)
+
2
x
)
c. (iii)
lim
x
→
−
2
(
x
4
+
4
x
3
+
6
x
2
+
4
x
+
1
)
\displaystyle \lim_{x \to -2} \bigl(x^{4}+4x^{3}+6x^{2}+4x+1\bigr)
x
→
−
2
lim
(
x
4
+
4
x
3
+
6
x
2
+
4
x
+
1
)
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