Units 1 and 2
If Limx->a= b, does f(a) = b?
No
The acceleration of a car at 1 second whose position in meters is determined by f(t) = e-x + sqrt(x) - 1
[-1/4 + e-1] m/s2
The integral of 1/x2 from x = -2 to x = 3 with respect to x
Diverges
The process of separation of variables in the context of differential equations
Rearranging a differential equation such that each of the two variables are on a different side of the equation. Then, integrating both sides and solve for y.
The other classes Ms. Contreras teaches
Linear algebra and MAPS
The limit definition of a derivative
Limx->0 (f(x+h) - f(x))/f(x)
or
Limx->a (f(x) - f(a))/(f-a)
dy/dx of y3+y=x at (10,2)
1/13
The indefinite integral of arcsin(x) dx
x arcsin(x) + √(1−x2) + C
dy/dx = 2xy
y = ?
y = ex^2 + C
Name of the math class the Ms. Contreras took most recently and the grade that she recieved.
Combinatronics, B+
The definition of continuity
Limx->a = F(a) & F(a) exists
d2149/dx2149(sin(5x)) =
52149cos(5x)
The maximum of sin(x)ex on [0,2π]
sin(3π/4)e3π/4
This type of differential equation represents bounded growth
Logistic growth
The number of subscribers that the Grace Contreras YouTube channel has. Specifically the one that has all of the videos from the beginning of the year.
21
d/dx[x3/(ex + sinx)]
3x2(ex + sinx)-1 - x3(ex + sinx)-2(ex + cosx)
Limx->0(cos(x))1/x
1
The indefinite integral of sin(ln(x)) with respect to x
[x( sin(ln(x)) - cos(ln(x)) ) / 2] + C
Average Value of y = (x+2)3 from x = 1 to x = 3:
68
The value of the sealed Albert Einstein action figure next to Ms. Contreras' desk.
approximately $15 (will accept answers within 5 dollars)
Limx->2[ln(x2-4)-ln(x-2)]
ln(4)
d/dx[xcos(x)]
xcos(x)[cos(x)/x - ln(x)(sin(x)]
Point of relative maximum of the graph:
Sin2(x2) on the interval [0, 2π/3]
1.253
or
√(π/2)
A function y exists such that
dy/dx = ey-x(x2-1) & y(-1) = 1
y = -ln(e-x(x+1)2+e)
The profession of Ms. Contreras' father
Pediatric hematologist