Chapter 2
Find the limit of
lim x-6
x->6 x2-36
What is 1/12
Differentiate with respect to x.
y= 4x5+x
What is 20x4+1
Find the critical points.
f(x)=8x3-x2
What are x=0 and x=1/12
Estimate the area under the graph of f(x)=1+x2 from x=-1 to x=2 using three rectangles and a right endpoint approximation.
What is 8
Find the area of the region enclosed by the graphs of f(x)=x2+2 and g(x)=2x.
What is 10.66
Find the limit of
lim 3x2+4x-1
x->∞ 2x2-5x-2
What is 3/2
Find f' (x) when f(x)=(4x3+2x2+8)(2x2-6x).
What is 40x4-80x3-36x2+32x-48
Find the intervals on which f is concave up or down. Find the points of inflection.
y=x3-6x2+4
What is (-∞, 2) concave down, (2, ∞) concave up, and p.o.i. @ x=2
Estimate the area under the graph of f(x)=1+x2 from x=-1 to x=2 using three rectangles and midpoint approximation.
What is 5.75
Find the area of the region bounded by x=y2-2 and x=y.
What is 4.5
Find the limit of
lim sin(10x)
x->0 x
What is 10
Find f''' (3) when f(x)=-2ex-8x3.
What is -2ex-48
Find the critical points.
f(x)=sinx+cos2x on [0, 2π]
What are x=π/2, x=3π/2, x=π/6, and x=5π/6
Evaluate the definite integral
32
∫ x-6/5dx
1
Find the area of the region bounded by the intersections of the curves.
y=x2-1, y=7-x2
What is 21.3
A ball is tossed vertically into the air from ground level with an initial velocity of 10m/s. Its height (in meters) and time t (in seconds) is given by the function h(t)=10t-4.9t2. Estimate the ball's instantaneous velocity at t=1.
What is .2 m/s
Differentiate with respect to x.
y= 2
2x4-5What is 16x3
4x8-20x4+25
Use L'Hôpital's rule to evaluate
lim x3-8
x->2 x4+2x-20
What is 6/17
Evaluate the definite integral using U substitution.
u=5x+4
du=5dx
∫(5x+4)5dx
What is (5x+4)6 +c
30
Find the volume of the solid with a base enclosed by x+y=1 with cross sections perpendicular to the y-axis being semi circles.
What is .13
Find the limit as it approaches infinity.
lim 20x2-3x
x->∞ 3x5-4x2+5
What is 0
A truck enters the offramp of a highway at t=0. Its position after t seconds is s(t)=25t-0.3t3m for 0<t<5. How fast is the truck moving at the moment it enters the offramp?
What is V(0)=25 m/s?
Find the indefinite integral.
f(x)=9x+15x-2
What is
9x2 -15x-1 +c
2
Evaluate the definite integral using U substitution.
u=4x-1
du=4dx
∫x√(4x-1) dx
What is (4x-1)5/2 + (4x-1)3/2 +c
40 24
The region bounded by the graph of y=2x-x2 and the x-axis is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a triangle with a height 3x the base. What is the volume of the solid?
What is 1.6