Limits at infinity
As x-> infinity, what is the limit of the function:
f(x)=(x+5)/(3x+1)
What is (1/3)?
As x->3, what is the limit of the function
f(x)=(2x^2-6x)/(x-3)
What is 6?
Find the derivative.
f(x)=3x^2+5x−2
6x+5
What is the calculus definition of continuity?
What is the limit of a function at a point must equal the value of the function at that point?
The position of an object moving along a straight line is given by
s(t)=3t^2-2t+1
where s is in meters and t is in seconds. Find the velocity of the object at t=2 seconds.
10 m/s
As x->infinity what is the limit of the function
f(x)=(100x+7)/(5x^2-2x+1)
What is zero?
As x->3, what is the the limit of the function
f(x)=(2x-6)/(x^2-3x)
What is (2/3)?
Find the derivative.
g(x)= sqrtx + 1/x
1/(2sqrtx) -1/x^2
What is the location and type of discontinuity of this function?
f(x)=2x-x^3
Continuous. Polynomials are continuous everywhere
An object's velocity is given by the function below where t is time in seconds. Find the acceleration of the object at t=4 seconds.
v(t)=6t^2-3
48 m/s2
As x-> infinity, what is the limit of the function
f(x)=(x^2+4x+10)/(5x-2)
As x->0, the limit of the function
f(x)=(4x^2-8x)/(2x^2-3x)
What is 8/3?
Find the derivative.
(2x+1)(3x^2 −4)
18x ^2 +6x−8
What are the locations and types of discontinuities of this function?
f(x)=(x+7)/((x-7)(x+7))
What is x=7 infinite and x=-7 Point?
Given the curve
f(x)=3x^2-2x+1
find the slope of the tangent line to the curve at the point where x=2
10
As x-> infinity what is the limit of the function
f(x)=(2/x+5)*((4x^3-5x+1))/(-7x^3-3)*(1-x/(2x+1))
What is -10/7?
As x->-1, what is the limit of the function
f(x)=(x^2-3x+2)/(x+1)
What is does not exist?
Find the Derivative.
(x^2-2x+1)/(x+1)
(x^2+2x-3)/(x+1)^2
What is the location and type of discontinuity of this function
f(x)=abs(5x-2)/(5x-2)
What is x=2/5 jump?
Consider the function below. Determine the slope of the secant line that passes through P (1,f(1)) and Q (3,f(3))
f(x)=x^2-3x+2
1
As x-> infinity, what is the limit of the function (hint: we did this when looking at exponential derivatives)
f(x)=(1+1/x)^x
What is e?
As x->3/2, what is the limit of the function
f(x)=(2x-3)/(10x^2-13x-3)
What is (2/17)?
Find the derivative.
g(x)=cos(2x ^2 +3x)
−sin(2x^2 +3x)⋅(4x+3)
What is the location and type of discontinuity?
f(x)= (x^3-8)/(x^2-4)
Not continuous as x=-2, Vertical Asymptote
For the curve below. Find the equation of the tangent line to the curve at the point where x=2
y=("x^3/3)+1/x
y=15/4x-13/3