Find the equation of the straight line passing through the point (0, 2)

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

8 0

Answer:

y = -4x+2

Step-by-step explanation:

y = x/4+5

y = 1/4(x+20)..........................1/4 is our gradient here

if parallel same gradient

if perpendicular, m1 *m2 = -1 ........where m1 is the gradient and m2 perpendicular gradient

1/4 * m2 = -1

m2 = -4

<em>if passes through ( 0,2)</em>

y-2 = -4(x-0)

y = -4x+2

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Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integr

prisoha [69]

Split up the interval [0, 2] into 4 subintervals, so that

$[0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right]$

Each subinterval has width $\dfrac{2-0}4=\dfrac12$ . The area of the trapezoid constructed on each subinterval is $\dfrac{f(x_i)+f(x_{i+1})}4$ , i.e. the average of the values of $x^2$ at both endpoints of the subinterval times 1/2 over each subinterval $[x_i,x_{i+1}]$ .

So,

$\displaystyle\int_0^2x^2\,\mathrm dx\approx\dfrac{0^2+\left(\frac12\right)^2}4+\dfrac{\left(\frac12\right)^2+1^2}4+\dfrac{1^2+\left(\frac32\right)^2}4+\dfrac{\left(\frac32\right)^2+2^2}4$