Question

HELP!!!!!
The figure below shows a Riemann sum approximation with n subdivisions to EQUATION.

Is this a left or right hand approximation?
What are the following?
a=
b=
n=
triangle x=

Answer 1

EQUATION in problem\[\int\limits_{a}^{b}f(x)dx\]

Answer 2

can you help me

Answer 3

@tcarroll010 can you help me

Answer 4

as you can see the rectangles only approximate the area under the curve.
the left side of each rectangle touches the curve. that tells you it is a left-hand approximation

Answer 5

right I knew that but I don't know what all the letters equal

Answer 6

I think a is the lower bound, and b is the upper bound of the region they want to integrate
n is the number of rectangles

Answer 7

a=.5
b=3.4
n=8
is that correct can you check me

Answer 8

the integral
\[\int\limits_{a}^{b} f(x) dx\]
starts at a and goes to b. Those are the x values
you want the smallest x value (left side) of the first rectangle.
and the largest x value (right side) of the last rectangle.

Answer 9

a=.5
b=4
n=8
now good

Answer 10

yes, except I think the low limit is 0

Answer 11

a=0b=4 and n=8 you mean that

Answer 12

yes

Answer 13

then what is the triangle x=

Answer 14

I don't know what they mean by triangle x

Answer 15

symbol triangle then x

Answer 16

change in x maybe

Answer 17

that is what I mean

Answer 18

phi do you know now what it could equal

Answer 19

oh, in that case it is "delta x"
(Greek letter for D)
it is standard terminology for the width of the rectangle

Answer 20

so you mean like4

Answer 21

no, \(\Delta x\) is the width of one rectangle (not all of them together)

Answer 22

so like 1

Answer 23

or.5

Answer 24

each rectangle has a width of 0.5, so \( \Delta x\)= 0.5 for this problem

Answer 25

ok thanks

Answer 26

The idea is they are teaching you that in calculus, you are adding up the area of a bunch of rectangles. The key idea is the \(\Delta x\) is *very* tiny in calculus.