4.Question:
(a)
(b)
(c)
(d)
Calculate the derivative of: F(x)=ln(cos(3x)
Calculate the derivative of: G(x)=(e*sin(ex)*cos(x+x2)
Calculate the derivative of: H(x)= (ecos4xn
+ln *cos(x)2
More generally, show that if f,g,and h are differentiable, then :
[f(g

3. Problem Statement: Suppose f(x) is a piecewise function defined as follows:
f(x)=
2x2+2
,if x<1
2
ax +bx ,if 1x2
2- (6/x)
. if x>2
a) Suppose that a=2 and b=-3. Graph f(x) for 0 x 3. Find the left and
right hand limits of f(x) as x approaches 1 and as

3. Problem Statement: Suppose f(x) is a piecewise function defined as follows:
f(x)=
2x2+2
,if x<1
2
ax +bx ,if 1x2
2- (6/x)
. if x>2
a) Suppose that a=2 and b=-3. Graph f(x) for 0 x 3. Find the left and
right hand limits of f(x) as x approaches 1 and as

1.Problem Statement: Two circles have the same center. The inner circle has radius r which is
increasing at the rate of 3 inches per second. The outer circle has radius R which is increasing at
the rate of 2 inches per second. Suppose that A is the area o

Raymond Wan
Calculus 151
Workshop #7
David Sheiman
11/3/16
1. Problem Statement: A square and a circle are placed so that the circle is outside the
square and tangent to the one side of the square. The sum of the length of side of the
square and the circl

4.Question:
a) If you substitute h by -h in the definition of derivative, what conclusion will you get?
b) Now take the average of the FDQ and BDQ, what conclusion can you draw from this?
Can we define the derivative by taking the limit of SDQ?
c) Conside

4. Problem Statement Suppose that f is the function defined by the formula
f(x)= (arctan(ln(x-1)3
A) What are the domain and range of f? Answers should not be numerical approximations,
but should be written if needed in terms of traditional constants such

3. Problem statement: An object is moving along the parabola y=3x2.
a) When it passes through the point (2,12), its horizontal velocity is dx/dt= 3. What is its
vertical velocity at that instant?
b) If it travels in such a way that dx/dy=3 for all t, then