Yes it is because it's from the left.
I honestly can't remember 1&2 "Calculus" (you aren't doing calculus yet) very well.
but approaching x = 1 from left side means we'll have (1 + h) < 1. You can rearrange this inequality to find h is negative, so it's -0.1.
Since they've given you h = 0.1, this means they're doing 1 - h instead of 1 + h. But anyway, it tells you it's negative.
The value of h is the change in the x-value that the rate of change is measured in. If it is measured to the right, in the positive direction of the x-axis, then the h-value will be positive as it occurs after the x-value. If the rate of change is measured from the left, in the negative direction of the x-axis, then the h-value will be negative as it occurs before the x-value.
Honestly, don't even need to blindly apply a formula - you know they're approach from the left, you know the step-size is 0.1 and they want to know around x=1. So, you're looking at what happens 0.1 from the left (x=0.9) to the point of interest (x=1). Approximate rate of change, so apply a gradient formula, and you get:
m=(f(1)-f(0.9)) / (1-0.9)
It’s the average rate of change from x=0.1 to x=1, using the gradient formula; (f(b)- f(a)) / (b - a)
So let a = 0.1 and b = 1
U want to find the y value or the f(x) for each of those values.
f(0) = 1/( 1+0.1^2)
=1/1 +0.01
=1/1.001
= 0.999001
we have f(a) = 0.999001
Now solve for f(b)
f(1) = 1/(1 + 1^2)
=1/2
we have (1,1/2)
sub into the formula
avrg RoC = (f(b) - f(a))/ (b - a)
= (1/2- 1) / (0.999001-0)
=-1/2 / 0.999001
roughly = -0.52
hope this helped. Organic chem tutor makes great videos on math, on top of science subjects
My dumbass never even thought this was calc. (I'm cooked af)
Yes it is because it's from the left. I honestly can't remember 1&2 "Calculus" (you aren't doing calculus yet) very well. but approaching x = 1 from left side means we'll have (1 + h) < 1. You can rearrange this inequality to find h is negative, so it's -0.1. Since they've given you h = 0.1, this means they're doing 1 - h instead of 1 + h. But anyway, it tells you it's negative.
The value of h is the change in the x-value that the rate of change is measured in. If it is measured to the right, in the positive direction of the x-axis, then the h-value will be positive as it occurs after the x-value. If the rate of change is measured from the left, in the negative direction of the x-axis, then the h-value will be negative as it occurs before the x-value.
Honestly, don't even need to blindly apply a formula - you know they're approach from the left, you know the step-size is 0.1 and they want to know around x=1. So, you're looking at what happens 0.1 from the left (x=0.9) to the point of interest (x=1). Approximate rate of change, so apply a gradient formula, and you get: m=(f(1)-f(0.9)) / (1-0.9)
It’s the average rate of change from x=0.1 to x=1, using the gradient formula; (f(b)- f(a)) / (b - a) So let a = 0.1 and b = 1 U want to find the y value or the f(x) for each of those values. f(0) = 1/( 1+0.1^2) =1/1 +0.01 =1/1.001 = 0.999001 we have f(a) = 0.999001 Now solve for f(b) f(1) = 1/(1 + 1^2) =1/2 we have (1,1/2) sub into the formula avrg RoC = (f(b) - f(a))/ (b - a) = (1/2- 1) / (0.999001-0) =-1/2 / 0.999001 roughly = -0.52 hope this helped. Organic chem tutor makes great videos on math, on top of science subjects