Answered

Discover new knowledge and insights with IDNLearn.com's extensive Q&A database. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

(1+h): - 1
A. lim
h>0
h
f(0) =
х
a =
1
B. lim
h>0
cos(1 + h) +1
h
f(3) =
a =
7T
5(4+ h)" - 5120
C. lim
h->0
h
f(x) =
a =
4
o
D. lim
h 0
e4h - 1
h
f(x) =
a =
e
Х
Pls take a look at the picture

1h 1 A Lim Hgt0 H F0 Х A 1 B Lim Hgt0 Cos1 H 1 H F3 A 7T 54 H 5120 C Lim Hgt0 H Fx A 4 O D Lim H 0 E4h 1 H Fx A E Х Pls Take A Look At The Picture class=

Sagot :

LammettHashidn

Each of these limits correspond to the derivative of some function f(x) at a point x = a.

Recall the limit definition of a function f(x) :

f '(x) = lim [h → 0] ( f(x + h) - f(x) ) / h

Then if x = a, we get

f '(a) = lim [h → 0] ( f(a + h) - f(a) ) / h

From here, it's easy to identify what each function and point should be:

(a) f (a + h) = (1 + h)¹ʹ³   →   f(x) = x ¹ʹ³ and a = 1

(that's a 1/3 in the exponent)

(b) f (a + h) = cos(π + h)   →   f(x) = cos(x) and a = π

(c) f (a + h) = 5 (4 + h)⁵   →   f(x) = 5x ⁵ and a = 4

(d) f (a + h) = exp(4h) = exp(4 (0 + h))   →   f(x) = exp(4x) and a = 0

(where exp(x) = eˣ )

Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.