Step-by-step explanation:
The Taylor series expansion is:
Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!
f(x) = 1/x, a = 4, and n = 3.
First, find the derivatives.
f⁽⁰⁾(4) = 1/4
f⁽¹⁾(4) = -1/(4)² = -1/16
f⁽²⁾(4) = 2/(4)³ = 1/32
f⁽³⁾(4) = -6/(4)⁴ = -3/128
Therefore:
T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!
T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³
f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. So we can eliminate the top left option. That leaves the other three options, where f(x) is the blue line.
Now we have to determine which green line is T₃(x). The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).
The bottom right graph is the only correct option.
Answer:
y=5x+(-19)
Step-by-step explanation:
Refer to the picture that given
Answer:
prime factorization of 28
28 = 2 × 2 × 7
prime factorization of 50
50 = 2 × 5 × 5
Step-by-step explanation:
GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2
Answer: The Nth power xN of a number x was originally defined as x multiplied by itself, until there is a total of N identical factors. By means of various generalizations, the definition can be extended for any value of N that is any real number.
(2) The logarithm (to base 10) of any number x is defined as the power N such that
x = 10N
(3) Properties of logarithms:
(a) The logarithm of a product P.Q is the sum of the logarithms of the factors
log (PQ) = log P + log Q
(b) The logarithm of a quotient P / Q is the difference of the logarithms of the factors
log (P / Q) = log P – log Q
(c) The logarithm of a number P raised to power Q is Q.logP
log[PQ] = Q.logP
Step-by-step explanation:
Answer: b) two sides and the included angle are congruent
<u>Step-by-step explanation:</u>
RS = QS SIDES are congruent
∠PSR ≡ ∠PSQ ANGLES are congruent
PS = PS SIDES are congruent
ΔPSR ≡ ΔPSQ by the Side-Angle-Side (SAS) Congruency Theorem
Since we know the triangles are congruent, we can state that their parts are congruent:
Congruent-Parts of-Congruent-Triangles are-Congruent (CPCTC)