Vectors
Rates Of Change And Limits
Derivatives
Curve Sketching and Optimization
Derivatives Of Trig And Exponential Functions
100
Write the true bearing as a quadrant bearing. 275° .
N 85° W
100
Given the equation -9.8t2-4.9t, estimate the IRoC at a height of 2 s.
-19.6 m/s
100
Differentiate the following. y=2x6-5x3+12
y'=12x5-15x2
100
Find the x-intercepts and y-intercepts for the function f(x)=x2+4
y= 4 , x= no roots
100
Differentiate. y=5 sin x
y'=5 cos x
200
Calculate the work being done if you pull a wagon at an angle of 30 degrees to the for 80 m with a force of 130 N. Round to 1 decimal place.
1604.2 J
200
Given the equation -9.8t2-4.9t, find the ARoC in the interval from 1 s to 5 s.
-63.7 m/s
200
Find the second derivative. y=3x4+5x2+8x+3
y"=36x2+20x
200
Find the vertical and horizontal asymptote for the function f(x)= x/(x2 -4).
V.A= 2 and -2, H.A= 0
200
Differentiate. y= 3cos x - 2sin x
y'= -3 sin x - 2 cos x
300
Determine |3
-2
| given that =3, and =6 and the angle between the two vectors is 60° given that the two vectors are arranged tail to tail.
3-2= 20.8 units and θ= 30°
300
A box is pushed over the edge of a railing and follows the equation: h(t) = 50-4.9t2. Find an expression that represents the velocity of the box as it falls.
= -9.8t
300
Differentiate. g(x)= 12x4-6cos(x)
g'(x)=-48x3 +6sin(x)
300
Find the max/min values and intervals of inc/dec for the function f(x)= x2+4.
Max= (0,4). Intervals of inc is x>0, and intervals of dec is x<0.
300
Find the slope of the tangent to the graph of f(x) = 4sin x at the point where x = π/4
2√ 2
400
Find the scalar equation of the plane containing the points A(-2,-1,-4), B(3,6,2), and C(5,-2,4).
62x+2y-54z+90=0
400
Find the limit limx->2(6x2+5x+2).
36
400
Differentiate. f(x)=x2/(x-1)
f'(x)=x(x-2)/(x-1)2
400
Find concavity and points of inflection for the function f(x)= x2+4.
Points of inflection= none
Always concave up
400
Find the derivative of y = 2sin3x - 4cos2x
6sin2x cosx + 8 cosx sinx
500
Determine the POI for the three planes.
5x-2y-7z-19=0
x-y+z-8=0
3x+4y+z-1=0
POI = (4,-3,1)
500
Find the limit. limx->1 √ (x+3) -3 .
-1
500
Determine the equation of the tangent line at x=1 to the curve y=2x3 .
m=6
y =6x - 4
500
When the degree of the numerator is greater than the degree of the denominator you get one of these.
oblique asymptote
500
Evaluate: 4ln e6 + 4log 1000
36