7. EXPONENTIAL FUNCTIONS AND THEIR DERIVATIES (1) Recall the definition of an exponential function. First, the basics. Let a be a positive real number. Then • for n a positive integer, a" = for n = 0. a" = ● • for n a negative integer, say n = -k, a" • for x = a rational number, a* = P 9 for x an irrational number, a" = • a-y (at)v (ab) (2) Properties of exponents: For any real numbers x, y and a, b positive real numbers, • a+y . 0⁰ (3) Let f(x) = b. Here b is called MTH 32 . What happens when b<0? . What happens when b = 0? . What happens with b= 1? Explain in detail. and r is called the 37
7. EXPONENTIAL FUNCTIONS AND THEIR DERIVATIES (1) Recall the definition of an exponential function. First, the basics. Let a be a positive real number. Then • for n a positive integer, a" = for n = 0. a" = ● • for n a negative integer, say n = -k, a" • for x = a rational number, a* = P 9 for x an irrational number, a" = • a-y (at)v (ab) (2) Properties of exponents: For any real numbers x, y and a, b positive real numbers, • a+y . 0⁰ (3) Let f(x) = b. Here b is called MTH 32 . What happens when b<0? . What happens when b = 0? . What happens with b= 1? Explain in detail. and r is called the 37
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:and explain the range and domain for each.
function (or the arctan function). Draw the relevant graphs
7. EXPONENTIAL FUNCTIONS AND THEIR DERIVATIES
(1) Recall the definition of an exponential function. First, the basics. Let a be a positive real
number. Then
• for n a positive integer, a" =
• for n = 0. a" =
for n a negative integer, say n = -k, a" =
• for x =
a rational number, at
1
9
. for x an irrational number, a" =
• =
at-y
(aª)³ =
(ab) =
I
(5)
●
P
-
=
be inaction
(2) Properties of exponents: For any real numbers x, y and a, b positive real numbers,
• a+y =
00
(3) Let f(x) = b. Here b is called
MTH 32
• What happens when b< 0?
. What happens when b = 0?
What happens with b = 1?
Explain in detail.
37
and x is called the
64
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