Unit 1
The limit as x approaches infinity of
[x2 + 4x5 - 3]/5x5 + 3x
4/5
y = tan(x)cos(x)
Find y'
y' = cos(x)
y = e4x^3 Find y'
y' = 12x2e4x^3
The position of a particle moving along a coordinate line is s(t) = 2t3 - 6t, with s in meters and t in seconds. Find the particle's velocity and acceleration at t = 6.
V(6) = 210
A(6) = 72
The function defined by g(x) = 4x3 - 3x2 for all values of x has a relative maximum at x =
0
limit as x approaches 0 of [√(x+19) - √19]/ x
1/2√19
Find the average rate of change on the interval
w(t) = 5t² - 5t +1; [-2, 1]
-10
ln(4y3) = 5x+3
Find dy/dx
dy/dx = 5y/3
Determine all the number(s) c which satisfy the conclusion of Mean Value Theorem for
A(t)=8t+e−3t on [−2,3] Use a calculator.
c = −1.097
What are the x-coordinate(s) of the points of inflection for the graph of 𝑓(𝑥) = sin(2𝑥) on the closed interval [0,𝜋]
x = 𝜋/4 and 3𝜋/4
Given f(x) = 3x2 - 2x + 5
Does the IVT guarantee that f(c) = 5 for some value c on the interval 1< c < 3
No 5 < f(1) < f(3)
f(x) = sin(x)/x²+1 Find f'(x)
f'(x) = (x2-1)cos(x) - 2xSin(x) / (x2-1)2
f(x) = cos(x) + 3x², f(𝜋/2) = 3𝜋2/4
if g(x) = f-1(x) find g'(3𝜋2/4)
g'(3𝜋2/4) = 1/(3𝜋 - 1)
A particle moves along a line so that its position at any time t ≥ 0 is given by the function s(t) =-t3 +7t²-16t + 8 where s is measured in meters and t is measured in seconds. When is the object Slowing Down.
Write the equation of a line tangent to the graph of f(x) = 2x³- 3x2 at its point of inflection is.
y + 1/2 = -3/2(x - 1/2)