5. Solve lim (x + e²a)1/a. Show complete solution. The following may be useful: x-0 ● ● lim ƒ(x)9(x) x→a (f(x) = g(x))' = f'(x) = g'(x) (sum rule) • (f g)' = f'g + fg' (product rule) • ((fog)(x))' = f'(g(x)) g'(x) (chain rule) ● dx d dx d C= 0 (derivative of a constant) dx d xn = In(x) n-1 nx" f (x) lim x→a g (x) lim g(x) In[f(x)] = exa =X - (power rule) I x-¹(derivative of the natural logarithm) f (x) x→a g(x) lim xa f'(x) g'(x) if lim M 0 0 or (L'Hôpital's rule)
5. Solve lim (x + e²a)1/a. Show complete solution. The following may be useful: x-0 ● ● lim ƒ(x)9(x) x→a (f(x) = g(x))' = f'(x) = g'(x) (sum rule) • (f g)' = f'g + fg' (product rule) • ((fog)(x))' = f'(g(x)) g'(x) (chain rule) ● dx d dx d C= 0 (derivative of a constant) dx d xn = In(x) n-1 nx" f (x) lim x→a g (x) lim g(x) In[f(x)] = exa =X - (power rule) I x-¹(derivative of the natural logarithm) f (x) x→a g(x) lim xa f'(x) g'(x) if lim M 0 0 or (L'Hôpital's rule)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![5. Solve lim (x + e²a)1/. Show complete solution. The following may be useful:
x 0
lim f(x)g(x)
x→a
(f(x) = g(x))' = f'(x) = g'(x) (sum rule)
(f g)' = f'g + fg' (product rule)
((fog)(x))' = f'(g(x)) g'(x) (chain rule)
d.x
d
d
c = 0 (derivative of a constant)
dx
d
dx
xn
=
lim g(x) In[f(x)]
nx"-1
= exa
-
(power rule)
I
-1
In(x) = x¯¹ (derivative of the natural logarithm)
f (x)
f (x)
f'(x)
x→a g(x) x→a g'(x) xa g(x)
lim
lim
if lim
0
0
or
818
(L'Hôpital's rule)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc0b8fd4-83f5-4ce5-b54d-512021d4fb00%2Fed9fbbd9-19b4-4cb1-a723-1981bc86132a%2F7q2tpzb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Solve lim (x + e²a)1/. Show complete solution. The following may be useful:
x 0
lim f(x)g(x)
x→a
(f(x) = g(x))' = f'(x) = g'(x) (sum rule)
(f g)' = f'g + fg' (product rule)
((fog)(x))' = f'(g(x)) g'(x) (chain rule)
d.x
d
d
c = 0 (derivative of a constant)
dx
d
dx
xn
=
lim g(x) In[f(x)]
nx"-1
= exa
-
(power rule)
I
-1
In(x) = x¯¹ (derivative of the natural logarithm)
f (x)
f (x)
f'(x)
x→a g(x) x→a g'(x) xa g(x)
lim
lim
if lim
0
0
or
818
(L'Hôpital's rule)
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