Algebra I & II
Solve for x:
2x + 3 = 9
x = 3
Evaluate:
sin(45)
sqrt(2)/2
What room number are we currently in?
3215
Find the limit as x approches 0:
sin(x)/x
limit = 1
Find the derivative of the following:
f(x) = cos(7x)
-7sin(x)
x2 - 5x + 6
x = 2 and x = 3
Find the equation of the line that passes through the points (2,3) and (4,7).
y = 2x - 1
I am the product of six times four minus six. My digits add to nine. What number am I?
18
Find the derivative of the following functions:
r(x) = x2; s(x) = sin(x); t(x) = ex
r'(x) = 2x
s'(x) = cos(x)
t'(x) = ex
What is the limit of the function f(x) = (csc(x) - cot(x) + cos(x)) as x approaches 0 from the right?
(sin(x) - sin2(x) + cos2(x))/(cosx)
Divide 2x3 - 3x2 + 4x - 5 by x - 2
2x2 + x + 2 + 3/x-2
Simplify the complex number:
(3 + 2i)(4 - 5i)
22 - 7i
If we are given v(t), how do we find a(t)?
Take the derivative of v(t)
Use implicit differentiation to find dy/dx:
x2 + xy + y2 = 7
dy/dx = (-2x-y)/(x+2y)
f(x) = tan(x)/csc(x)
What is f'(x)?
f'(x) = sec2(x)csc(x) - csc(x)
Common ratio: 2
Find the domain:
f(x) = sqrt(5-x)
x is less than or equal to 5
What was the mathematical object that Colby K talked about at one of our previous meetings?
Gabriel's Horn
Find the derivative:
f(x) = e2xsin(x)
f'(x) = 2e2xsin(x) + e2xcos(x)
What is f'''(x) when
f(x) = 2x6 - 5x5 + 12x3 - 15x + 27
240x3-300x2+72
Solve for x:
log2(x-1) + log2(x+1) = 3
x = 3
Extraneous: x = -3
Determine the polar coordinates of the point (-2sqrt(3), 2) where r is positive and 0 ≤ θ < 2pi.
(-4, -pi/6)
OR
(4, 5pi/6)
I am always coming, but never here, never arriving, but always near. What am I?
Tomorrow
Find the integral of the following functions:
r(x) = 2x; s(x) = cos(x); t(x) = ex
r(x) = x2
s(x) = sin(x)
t(x) = ex
Evaluate the improper integral with bounds from 1 to infinity:
(ln(x)/x2)dx
-1