"if x=2,f(x)=1if x=3,f(x)=4if x=5,f(x)=−2if x=8,f(x)=3if x=13,f(x)=6f is twice..." was answered by students like you

High School
Geometry
Trigonometry
Trigonometric Functions

Tazmin Horton

Answered question

2021-09-06

if $x = 2, f (x) = 1$
if $x = 3, f (x) = 4$
if $x = 5, f (x) = - 2$
if $x = 8, f (x) = 3$
if $x = 13, f (x) = 6$
f is twice variable for all real numbers.
1. Find $f^{'} (4)$
2. Approximate ${\int_{2}}^{13} f^{'} (x) d x$
2. Find the value of ${\int_{2}}^{8} (3 - f^{'} (x)) d x$

Answer & Explanation

faldduE

Skilled2021-09-07Added 109 answers

1. $f^{'} (4) = \frac{f (5) - f (3)}{5 - 3}$
$= \frac{- 2 - 4}{2}$
$= - 3$
2. The lengths of intervals are 1, 2, 3, and 5 respectively. Right end points:
$\underset{1}{x} = 3, \underset{2}{x} = 5, \underset{3}{x} = 8, \underset{4}{x} = 13$
Use Riemann Sum:
$\underset{4}{R} = f (3) \times 1 + f (5) \times 2 + f (8) \times 3 + f (13) \times 5$
$\underset{4}{R} = 4 - 2 \times 2 + 3 \times 3 + 6 \times 5$
$\underset{4}{R} = 39$
3. (C)
${\int_{2}}^{8} (3 - f^{'} (x)) d x = {\underset{2}{[3 x - f (x)]}}^{8}$
$= 3 \times 8 - f (8) - 3 \times 2 + f (2)$
$= 24 - 3 - 6 + 1$
$= 16$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Trigonometry

Didn't find what you were looking for?