definitions
a function is said to be continuous at x if:
what is the limit exists and is equal to the function value, in other words, if limx->a f(x) = f(a).
the limit of f(x) = (x^2+3)/(2x^3-7) at x = 2:
what is 7/9?
The derivative of y = 3x^2 - 4 (make sure you write the answer as an equation):
what is dy/dx = 6x?
the sign function sgn(x) can be written as 3 cases:
what is:
1. sgn(x) = 0, if x=0
2. sgn(x) = -1, if x<0
3. sgn(x) = 1, if x>0?
the terminology for these forms 0/0, 0*∞, ∞/∞:
what is indeterminant forms?
the limit definition of the derivative of f(x)
what is limh->0 f(x+h)-f(x)/h?
three ways(tricks) we can solve limits:
What is plugging in, factoring, and the conjugate method?
the derivative of f(x) = -6x^2 + 10x - 14 + tan(pi*x)
what is f'(x) = -12x + 10 + pi*sec^2(pi*x)?
the domain and range of: sin(ln(x))
what is (0, ∞), [-1,1]?
the condition for f(x) to be concave up/concave down:
what is f''(x)>0, f''(x)<0?
the name of the point when f'(x) = 0 & the name of the point when f''(x) = 0:
what is a critical point and an inflection point?
lim h->0 [(6+h)^2 - 36] / h:
what is 12?
The derivative of (cos3x)^5:
What is -15(cos3x)^4*(sin3x)?
the x-intercepts of y = x^3 + 6x^2 + 9x
what is 0 or -3?
the relationship between position s(t), velocity v(t), a(t)
what is s(t) = v'(t) = a''(t)?
the quotient rule for finding a derivative of f(x)/g(x):
what is (f'(x)g(x)-g'(x)f(x))/g(x)^2?
lim x->-5 (x^2 - 25) / (x^2 + 2x - 15)
what is 5/4?
the second derivative of sqrt(x) + e^(2x)
what is -1/(4*x^(3/2)) + 4e^(2x)?
we say a function f(x) is increasing/decreasing if:
what is f(x) gets larger as x gets larger/f(x) gets smaller as x gets larger?
(or f'(x)>0, f'(x)<0)
Let f(x) = (x^2-3)(2x), find the absolute maximum and absolute minimum of f(x) on the interval [-3,3]
what is 4x^2+2x^2-6 = 6x^2-6 = 0 -> x = +-1:
x = -3: f(x) = -36
x = -1: f(x) = 4
x = 1: f(x) = -4
x = 3: f(x) = 36
max at x = 3, min at x = -3
A function is said to be differentiable at x if:
what is x is in the domain of x and f'(x) exists?
lim x->4 (x^1/2 - 2) / (x - 4)
what is 1/4?
The equation of the tangent line to y = 2x^3 - 6 at x = 2:
What is y - 10 = 24(x-2)?
if the position of a person walking is represented as s(t) = (3t^2-7)/4 + 5 where t is time in seconds, the inverse of the function (and the meaning of it) is:
what is t = sqrt((4(s-5)+7)/3), interpreted as the corresponding time given a position of the person at s?
let the edge of the cube be x, assume that the volume of the cube is increasing at the rate of 10 cm^3 /minute. How fast is the surface area increasing when the edge length is 5 cm (include units)?
what is V = x^3, dV/dt = 3x^2 dx/dt= 10
-> 10 = 3(5)^2 dx/dt -> dx/dt = 10/75
A = 6x^2, dA/dt = 12x dx/dt = 12*5 *10/75 =8 cm^2/minute?