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)
12x ^2 +12x−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+4x+1)/(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
1/2
As x-> infinity, what is the limit of the function (hint: we did this in precalc when looking at continuous compounding)
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. Negative infinity from the left and positive infinity from the right.
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