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What is the derivative of 3x?
Let y = 3x y' = 3(x)' y' = 3(x1)' y' = 3[1x(1-1)] y' = 3(1x0) y' = 3(1 x 1) y' = 3 In general: y = xn y' nx(n-1)
Matrix inverse method ------ x1 x2 x33000 -x1 5x2-x30 2x1-3x30?
inverse matrix. x1+x2+x3=3,000 -x1+5x2=0 2x1-3x3=0.
X plus one over x squared plus two?
it equals x1 it equals x1
What is the definition of a point-slope form?
point slope form is y-y1=m(x-x1). x1 and y1 are both points and m is the slope.
State and prove Fundamental theorem of integral calculus?
This part is sometimes referred to as the First Fundamental Theorem of Calculus.Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b], byThen, F is continuous on [a, b], differentiable on the open interval (a, b), andfor all x in (a, b).ProofFor a given f(t), define the function F(x) asFor any two numbers x1 and x1 + Δx in [a, b], we haveandSubtracting the two equations givesIt can be shown that (The sum of the areas of two adjacent regions is equal to the area of both regions combined.)Manipulating this equation givesSubstituting the above into (1) results inAccording to the mean value theorem for integration, there exists a c in [x1, x1 + Δx] such thatSubstituting the above into (2) we getDividing both sides by Δx gives Notice that the expression on the left side of the equation is Newton's difference quotient for F at x1.Take the limit as Δx → 0 on both sides of the equation.The expression on the left side of the equation is the definition of the derivative of F at x1.To find the other limit, we will use the squeeze theorem. The number c is in the interval [x1, x1 + Δx], so x1 ≤ c ≤ x1 + Δx.Also, andTherefore, according to the squeeze theorem,Substituting into (3), we getThe function f is continuous at c, so the limit can be taken inside the function. Therefore, we get which completes the proof.
How do you simplify 3x-4x plus 9x-x?
Right, 3x-4x+9x-x1. 3x - x = 2x2. 9x-4x = 5x- 2x +5x = 7x
How do you solve for slope from two points and a graph?
Points: (x1, y1) and (x2, y2) Slope: y1-y2/x1-x2
What is the equation of a line that passes through (78) and has a slope of -3?
81
How do you solve a cubic?
Although there are formal methods, the simplest is to see if the cubic can be factorised. If so, you'll have a linear factor and a quadratic, both of which are easy to solve. Alternatively, you could try solving it graphically. Another possibility is to solve it numerically. The derivative of a cubic, of the form f(x) = ax3 + bx2 + cx + d is f'(x) = 3ax2 + 2bx + c. Make an initial estimate x1. An improved estimate is x2 = x1 - f(x1)/f'(x1). Use x2 to make next estimate, and so on.
What is 3x times x squared?
(3x)(x2) = 3x3.Think of this as (3x1)(1x2). First multiply the numbers: (3)(1) = 3. next multiply the variables: (x1)(x2) = x1+2 = x3 (when you multiply powers with the same base, add the exponents)
Explain how do you write an equation of a line in standard form when two points on the line are given?
Th e two points are X1,Y1 and X2, Y2 slope, m, is y2-y1 divided by x2-x1 then standard form is y = mx +b plug in y2 for y and x2 for x and solve b or plug in y1 for y and x1 for x and solve b
How do you differentiate y equals 6 sqrtx minus 3x?
y = 6*x1/2 - 3x dy/dx = 6*(1/2)*x-1/2 - 3 = 3x-1/2 - 3 = 3/sqrt(x) - 3 or 3[1/sqrt(x) - 1]
What are the Pokemon types of the elite 4 in Pokemon pearl?
Aaron Poison/Bug x1 Bug/Fighting x1 Bug/Flying x2 Poison/Dark x1 Bertha Water/Ground x2 Ground x1 Rock x1 Rock/Ground x1 Flint Fire x1 Fire/Fighting x1 Steel/Ground x1 Normal x1 Ghost/Flying x1 Lucian Psychic x2 Normal/Psychic x1 Fight/Psychic x1 Steel/Psychic x1 Cynthia Ghost/Dark x1 Dragon/Ground x1 Water/Ground x1 Water x1 Grass/Poison x1 Steel/Fighting x1
What are the coordinates of the y-intercept of the line represented by the equation 3x-4y equals 40?
3x-4y=40 (x=0) 3(0)-4y=40 -4y=40 y=40/-4 y=-10 x1 , y1 (13 , -10) (4y=0) 3x-4(0)=40 3x=40 x=40/3 x=13.33 or 13
How do you find a gradient of a line without a graph?
Select two values of x: (x1 and x2) within the domain. Solve the equation of the line to find the corresponding values for y: (y1 and y2). Then the gradient = (y1 - y2) / (x1 - x2)
What is the equation of the line that passes through 6 5 and -3 -1?
Point-Slope formula: y - y1=m(x - x1) y = 2/3x + 1
What is the equation of the line that passes through the point 4 -6 and haves a slope of -3?
We can use the point slope form.Y - Y1 = m(X - X1)----------------------Y - (- 6) = - 3(X - 4)Y + 6 = - 3X + 12Y = - 3X + 6============equation of the line
