Alternatively the equation x + y = 0 can be rewritten as x = ?y
If (x y) is a solution to the system of equations above
C) 1 b = -2. D) 7 f(-²) = 3(-8) - 2. -5 x=6 y. 4(y + 1) = x. If (x y) is the solution to the system of equations above
CROSS MULTIPLY. 160. Page 1 of 3. = 5?. A++. SLICK! In the equation above a is a constant. If no value of = PARALLEL x satisfies the equation
In the equation above which of the following is a possible value of x +1 ? A) 1? 2. B). 2. C) 2. D) 4.
hours spent cutting a lawn what are all the values of x for which Taylor's The equation above is used to model the relationship between the number.
1. Which of the following expressions is equal to 0 for if x=0 some value of x ? above? ?x-a =x- - 4. 2 what is the solution set of the equation.
Dividing each side of the equation 3r = 18 by 3 gives These equations do not correctly relate ... possible values of x are x = 1 and x = 2.
above. Which of the following statements must be true? (D) The graph of ƒ has a point of inflection at x=1.not necessarily don't know about values.
If -1 <y< 0 which of the following is not between -1 and 0? A) -1 - y If x satisfies the equation above
1 : tangent line equation (c) Vertical tangent lines occu r at points on the curve where y3 +=10 (or 1y =?) and 1 x ?? On the curve 1y =? implies that xx2 ++?=2145 so 4x =? or 2 x = Vertical tangent lines occur at the points ()??4 1 and ()2 1 ? 3 : 1 : 1 1 : substitutes 1 into the equation of the curve 1 : answer y y ? =?
Part (b) asked for an equation of the line tangent to the graph of f at the point where x =?3 Students needed to find the derivative at this point to determine the slope of the tangent line the y-coordinate of the graph of f at this point and then combine this information to provide an equation for the line
f are given for selected values of x in the table above (a) Write an equation for the line tangent to the graph of f at x = 1 Use this line to approximate f ()1 4 (b) Use a midpoint Riemann sum with two subintervals of equal length and values from the table to approximate () 1 4 1 f ? xdx Use the approximation for () 1 4 1
at a nearby value of x Students needed to recognize that the slope of the tangent line is the value of the derivative given in the differential equation at the given point Part (c) asked for the particular solution to the differential equation that passes through the given point
X (b)Let y = f(x) be the panicular solution to the given differential equation with initial condition f(l) = 0 Write an equation for the line tangent to the graph of y = f (x) at x = 1 Use your equation to approximate f (0 7) -:; l/ / [>Z-!) Ro1) Y/3 ( 0 +---1) Unauthorized copying or reuse of any part of this page Is Illegal 41 1( -fo)
curate approximations to the roots of the following quadratic equations Compute the relative error a) 1 3x 2 ? 123 4 x+ 1 6 =0; b) 1 002x2 +11 01x+0 01265 = 0 Solution: The quadratic formula states that the roots of ax2 +bx+c = 0 are x12 = ?b± ? b2 ?4ac 2a a) The roots of 1 3x 2 ? 123 4 x+ 1 6 = 0 are approximately x1 =92