2.6 and 3.6, Trig Limits and Derivatives
Exercise: Find the derivatives.
p
a) F (t) = 9 1 + tan(t)
b) H(x) = cos(37 + x 7 )
c) y = sin(tan(8x))
d) y = cos(cos(cos(x)))
e) y = (1 + sec(3πx + 4π))5
f) y = [x + (x + sin(2x))6 ]7
MATH 125
Lab: September 29, 2016
The University of Kansas
1/4
Exercise:
A mass on a spring vibrates horizontally on a smooth level
surface.
Its equation of motion is x(t) = 8 sin(t), where t is in
seconds and x is in centimeters.
(a) Find the position, velocity, and acceleration of the
mass at time t = 2π
3 .
(b) In what direction is the spring moving at that time?
MATH 125
Lab: September 29, 2016
The University of Kansas
2/4
Exercises:
Find an equation of the tangent line to the curve
y = sin(sin(x))
at the point where x = 3π.
MATH 125
Lab: September 29, 2016
The University of Kansas
3/4
Exercises:
Find an equation of the tangent line to the curve
y = sin(sin(x))
at the point where x = 3π.
Find the first and second derivatives of y = sin x 2 .
MATH 125
Lab: September 29, 2016
The University of Kansas
3/4
Exercises:
Find an equation of the tangent line to the curve
y = sin(sin(x))
at the point where x = 3π.
Find the first and second derivatives of y = sin x 2 .
Find all points on the graph of the function
f (x) = 2 cos(x) + cos(2x)
at which the tangent line is horizontal.
MATH 125
Lab: September 29, 2016
The University of Kansas
3/4
Exercise:
Solve the limits:
sin(6x)
(a) lim
x→0 cos(9x)
tan(16t)
(b) lim
t→0 sin(4t)
cos(7θ) − 1
(c) lim
θ→0
sin(9θ)
MATH 125
3 − 3 tan(x)
x→0 sin(x) − cos(x)
sin(x − 2)
(e) lim 2
x→2 x + 6x − 16
(d) lim
Lab: September 29, 2016
The University of Kansas
4/4