Question

Даны функции: 1)y=x^2+2x; 2)y=x^3-1. Найдите приращение y при x=3 и x=0.1

Answer 1

1)y=3^2+2*3
y=9+6
y=15
y=0.1^2+2*0.1
(1/10)^2+0.2
1/100+1/5
21/100
0.21
2)y=3^3-1
9-1
8
y=0.1^3-1
(1.10)^3-1
1/1000-1
999/1000

Answer 2

To find the increment (or the change in the value) of y for given values of x, we'll calculate the difference in the values of y at those specific x points.

Let's start with the first function:

1. y = x^2 + 2x

a) For x = 3: y = (3)^2 + 2(3) = 9 + 6 = 15

b) For x = 0.1: y = (0.1)^2 + 2(0.1) = 0.01 + 0.2 = 0.21

Now, let's move on to the second function: 2) y = x^3 - 1

a) For x = 3: y = (3)^3 - 1 = 27 - 1 = 26

b) For x = 0.1: y = (0.1)^3 - 1 = 0.001 - 1 = -0.999

So, the increments in y for x = 3 and x = 0.1 are as follows:

For x = 3: Increment in y = y(3) - y(0) = 15 - 26 = -11

For x = 0.1: Increment in y = y(0.1) - y(0) = 0.21 - (-0.999) = 1.209

Note: The term "increment" typically refers to the change in a quantity over a small interval. Here, we calculated the difference in y values at specific x points rather than small intervals.