limits (300 surprise)
What is the limit as x approaches 4 of 2x2-4x-7
9
What is the derivative of x2-4x
2x-4
There are 7 derivative rules given in your textbook (one kind of repeats). Name 6 of them
Derivative of a constant function, power rule, constant multiple rule, sum/difference rule, product rule, quotient rule, power rule for negative exponents
see pages 118-123
A particle moves along the x- axis so that any time t>0 its position is given by the function s(t)=4t3-2t2+1
At what time(s) does the the particle change directions?
t=0 (optional) and t=1/3
What is the limit as x approaches π/2 of sin(2x)
0
What is the derivative of 4/(x-1)
-4/(x-1)2
Just use power rule here for 4(x-1)-1
What is the intermediate value theorem for derivatives?
If and b are any two points in an interval on which f is differentiable, then f' takes on every value between f'(a) and f'(b)
See page 115
A particle moves along the x- axis so that any time t>0 its position is given by the function s(t)=4t3-2t2+1
What is the acceleration of the particle at time t=3? (give correct units!)
68 ft/s2
s''(t) = 24t-4
Does the curve x3 + 5x2 + 6 have any horizontal tangents? If so then where?
At x = 0 and x = -10/3
f'(x) = 3x2 + 10x = x(3x + 10) = 0
Find dy/dx for y = 5x-3 - 6x4 + 1/x
-15/x4 - 24x3 - 1/x2
What is the formula for the numerical derivative of f at a, in other words NDER( f(x) , a )
[f(a + 0.001) - f(a - 0.001)]/0.002
Find dy/dx for y = √x + 3/√x
y' = 1/(2√x) - 3/(2x3/2)
What is the limit as x approaches infinity of (1+1/n)n
2.71828...
Name 4 occasions (the terms) for when a function fails to have a derivative
corner, cusp, vertical tangent, discontinuity
(see page 111 of textbook)
The number of gallons in a tank is given by Q(t) = 250(40-t)2
How fast is the water leaking out after 10 minutes? (use correct units!)
15,000 gal/min
For what value of a would the limit exist for this piecewise function:
2x2-3+a x < 3
ax4-x3+3 x ≥ 3
a=39/80
Find derivative at x=5 of 2u/v if u(5) = 7, v(5) = 2, u'(5) = -3, and v'(5) = 6
-24
(vu' - uv')/v2
The number of gallons in a tank is given by Q(t) = 250(40-t)2
What is the average rate at which water flows out during the first 10 minutes? (use correct units!)
[Q(10)-Q(0)]/10 = (400,000 - 225,000)/10