1.1 A Preview of Calculus
Determine whether the problem can be solved using precalculus or calculus: Find the distance traveled in 15 seconds by an object moving with a velocity of v(t)=20+7 cos t
What is Precalculus
What is 5.99, 5.999, 5.9999, 6, 6.0001, 6.001, 6.01
Use a graphing utility to graph the function and visually estimate the limit
limx->-1=x2-5x
What is 6
Determine the continuity of the function
f(x)=1/(x2-4)
(Graphing Utility Allowed)
What is Discontinuous at x=-2 and x=2
Using the Given equation determine whether f(x) approaches infinity or negative infinity as x approaches -2 from the right
2|x/(x2-4)|
(Graphing Utility Allowed)
What is positive infinity
Find the are of a circle that center lies at (-2,1) and has outside point at (-1,0)
2π
State one of the three reasons why a limit might not exist
What is Behavior differs from the right and left, it is unbound, or oscillates
Determine the limit visually
limx->-1=(-2x2+x)/x
What is 3
Determine the continuity of the function on the closed interval
g(x)=√(25-x2), [-5,5]
What is continuous
Find the Limit if it exists
limx->1+(2+x)/(1-x)
(Graphing Utility Allowed)
What is negative infinity
Find the volume of a cylinder that has a radius for 3 and a height of 6
What is 54π
Find the Limit if it exists
Limx->5|x-5|/(x-5)
(Graphing Utility Allowed)
What is does not exist
Find the Limit
limx->14-x2
What is 3
Find the removable discontinuity of the function
f(x)=(x+2)/(x2-3x-10)
(Graphing Utility Allowed)
What is removable discontinuity at x=-2
Find the vertical asymptotes of the function
h(x)=(x2-2)/(x2-x-2)
What is x=2 and x=1
When estimating the length of a curve you can divide the curve into line segments than by finding the length of those segments you can estimate the length. Describe how you could continue this process to get a more accurate approximation of the length of the curve
What is adding more line segments
Informal Defintion of a limit
What is f(x) become arbitrarily close to L
Find the Limit
limx->4(√(x+5)-3)/(x-4)
What is 1/6
determine the continuity of the composite function h(x)=f(g(x))
f(x)=1/(x-6)
g(x)=x2+5
(Graphing Utility Allowed)
What is nonremovable discontinuities at x=1 and x=-1
Determine if the equation has a vertical asymptote or a removable discontinuity
f(x)=(x2-1)/(x+1)
What is a removable Discontinuity at x=-1
Describe how you might estimate the area underneath a curve without calculus
What is by dividing the area underneath into rectangles the finding the area of those and adding them
Actual Definition of a limit
What is for each ε>0 there exist a δ<0
Find the Limit of the trigonomic function if it exists
limx->5π/6 sin x
What is 1/2
True or False If f(x)=g(x) for x≠c and f(c)≠g(c), then either f or g is not continuous at c
What is true
Find the Limit
limx->-3-(x2+2x-3)/(x2+x-6)
What is 4/5