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3 years ago

Find and simplify the following for f(x) = x(19-x), assuming h+0 in (C).

Mathematics

1 answer:

alekssr [168]3 years ago

8 0

Answer: see below

Step-by-step explanation:

f(x) = x(19 - x)

= 19x - x²

A) f(x+h) = (x + h)[19 - (x + h)]

= (x + h)(19 - x - h)

= 19x - x² - 2xh + 19h - h²

B) f(x+h) - f(x) = (19x - x² - 2xh + 19h - h²) - (19x - x²)

= - 2xh + 19h - h²

= h(-2x + 19 - h)

C) [f(x+h) - f(x)]/h = [h(-2x + 19 - h)]/h

= -2x + 19 - h

As h → 0: = -2x + 19

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PLZ EXPLAIN AND I'LL GIVE BRAINLY!!!!

Nonamiya [84]

Hello there!

Given the sequence:

$\displaystyle \large{ 1, - 3,9, - 27,...}$

The question reveals it to be geometric sequence since it has common ratio.

Geometric Sequence / Ratio Formula

$\displaystyle \large{r = \frac{a_{n + 1}}{a_n} }$

Define 'r' as common ratio.

First, let's check the common ratio by using the formula above.

Ratio Check

$\displaystyle \large{r = \frac{ - 3}{1} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ 9}{ - 3} \longrightarrow - 3 } \\ \displaystyle \large{r = \frac{ - 27}{9} \longrightarrow - 3 }$

Therefore, the common ratio or r-value is -3.

To find the 7th term of sequence, you can by using the General Geometric Terms.

General Term of Geometric

$\displaystyle \large{a_n = a_1 {r}^{n - 1} }$

a1 is defined as the first term of sequence.

r is common ratio.

n is the term.

Since we want to find 7th term:

a1 = 1
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$\displaystyle \large{a_7 =1{( - 3)}^{7 - 1} } \\ \displaystyle \large{a_7 =1{( - 3)}^{6} } \\ \displaystyle \large{a_7 =729 }$

Therefore, the 7th term of this sequence is 729.

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