Limits
f(x) = 2x2 - 3x
lim f(x)x->-1 =
f(x) = 2x2 - 3x
lim f(x)x->-1 = 5
f(x) = 4x5
f'(x) =
f(x) = 4x5
f'(x) = 20x4
limx -> -1 (x2 + x - 2) / (x2 - 6x + 5) =
limx -> -1 (x2 + x - 2) / (x2 - 6x + 5) = -1/6
f(x) = csc(x)
f'(x) =
f(x) = csc(x)
f'(x) = -csc(x)cot(x)
An object moves along a straight line so that at any time t, for 0 <= t <= 8, its position is given by x(t) = 5 + 4t - t2
For what value of t is the object at rest?
An object moves along a straight line so that at any time t, for 0 <= t <= 8, its position is given by x(t) = 5 + 4t - t2
For what value of t is the object at rest?
t = 2
limx-> 3pi/2 (tan(x)) =
limx-> 3pi/2 (tan(x)) = DNE
f(x) = sin(pi*x2)
f'(x) =
f(x) = sin(pi*x2)
f'(x) = 2*pi*x*cos(pi*x2)
A particle moves along the x-axis so that at any time t >= 0, its position is given by x(t) = 1/2(a - t)2, where a is a positive constant. For what values of t is the particle moving to the right?
a) 0 < t < a
b) a < t
c) t = a
d) the particle is never moving to the right
A particle moves along the x-axis so that at any time t >= 0, its position is given by x(t) = 1/2(a - t)2, where a is a positive constant. For what values of t is the particle moving to the right?
a) 0 < t < a
b) a < t
c) t = a
d) the particle is never moving to the right
limx->0(cos(x) / x)
limx->0(cos(x) / x) = infinity -> DNE
y' =
y = sqrt(cos(x3))
y' = -(3x2sin(x3)) / 2*sqrt(cos(x3))
limx->0(sin(x) / x) =
limx->0(sin(x) / x) = 1
f(x) = [cos(4x) / 3x5]
f'(x) =
f(x) = [cos(4x) / 3x5]
f'(x) = -[4xsin(4x) + 5cos(4x)] / 3x6