(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

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 )

he sells x mount because thats eqivilqant to the maz and then divided into quarters

step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!