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 -9.8a-4.9h, 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)=2 over x2+4
y=1 over 2, x= no intercept
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 -9.8a-4.9h, find the ARoC in the interval from 1 s to 5 s.
-29.4 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)= 2 over x2+4.
V.A= None, H.A= 0
200
Differentiate. y= 3 cos x - 2 sin 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. The railing is 50 m above the ground. h(t) = 50-4.9t2. Find an expression that represents the height above the ground in terms of a and h.
= -9.8a-4.9h
300
Differentiate. g(x)= 12x4-6x3 over 3x2
g'(x)=8x-2
300
Find the max/min values and intervals of inc/dec for the function f(x)= 2 over x2+4.
Max= (0,2). 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) = 4 sin 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).
35
400
Differentiate. f(x)=x2-4 over 2x+5
f'(x)=2x2+10x+8 over (2x+5)2
400
Find concavity and points of inflection for the function f(x)= 2 over x2+4.
Points of inflection= (0.89, 0.42) and (-0.89, 0.42) Intervials for concave up are x<-0.89 and x>0.89. The concave down is -0.89<x<0.89
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) over x.
-1
500
Determine the equation of the tangent at x=1 to the curve y=2x over x+2.
y=2 over 9 x + 4 over 9
500
(100,200,300, and 400 must be completed first before attempting this question). Sketch the function f(x)= 2 over x2+4.
Plug in the function f(x)=2 over x2+4 on desmos.
500
Evaluate, using the laws of logarithms. 4log 6 + 4log 5
6.6