a) Evaluate the limit lim x→0 tan(2x) / x
b) Differentiate y = x^tan(x)
c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4
at the point (1, 2).
d) Differentiate f(x) = arctan(x^2 + 1)
e) Differentiate f(x) = ln(cosh x)
Thank you!
A graphing calculator is recommended.
For the limit
lim x → 2 (x3 −
2x + 4) = 8
illustrate the definition by finding the largest possible values
of δ that correspond to ε = 0.2 and ε =
0.1. (Round your answers to four decimal places.)
ε =
0.2
δ =
ε =
0.1
δ =
1) Find all of the second partial derivatives of
f(x,y)=3(x^4)y-2xy+5x(y^3).
2) Find an equation of the tangent plane to z=32-3(x^2)-4(y^2)
at the point (2,1,16).
(a) Find the limit of the following functions:
-lim as x approaches 0 (1-cos3(x)/x)
-lim as x approaches 0 (sin(x)/2x)
-lim as theta approaches 0 (tan (5theta)/theta)
(b) Find the derivative of the following functions:
-f(x) = cos (3x2-2x)
-f(x) = cos3 (x2/1-x)
(c) Determine the period of the following functions:
-f(x) = 3 cos(x/2)
-f(x)= 21+ 7 sin(2x+3)
1. . Find the limit: lim ?→ ∞ (? + √?2 + 2?)
2. If 1200 ??2 of material is available to make a box with a square
base and an open top, find the largest possible volume of the
box.
2. The volume of a right circular cone is ? =1/3 ??^2 ℎ , where ?
is the radius of
the base and ℎ is the height.
(a) Find the rate of change of the volume with respect to...
Find the limits, if they exist, or type DNE for any
which do not exist.
lim(x,y)→(0,0) (3x^2/(5x^2+4y^2))
1) Along the xx-axis:
2) Along the yy-axis:
3) Along the line y=mxy=mx :
4) The limit is: