-Use implicit differentiation to find dy/dx where
x2y2 + x cos(y) = 6
-Use logarithmic differentiation to find the derivative of o(x)
= (cos(x))ln(x)
-Find the first and second derivatives of p(x) = 6
ln(x2+3x)
-A balloon is rising vertically at a constant speed of 5 ft/sec.
A boy is
cycling along a straight road at a speed of 15 ft/sec. When he
passes
under the balloon, it is 45 ft above him.How fast is the
distance between
the boy...
Find dy/dx for a & b
a) sin x+cos y=1
b) cos x^2 = xe^y
c)Let f(x) = 5 /2 x^2 − e^x . Find the value of x for which the
second derivative f'' (x) equals zero.
d) For what value of the constant c is the function f continuous
on (−∞,∞)?
f(x) = {cx^2 + 2x, x < 2 ,
2x + 4, x ≥ 2}
evaluate
C
(y + 4 sin x)
dx + (z2 + 8 cos
y) dy +
x3dz
where C is the curve
r(t) =
sin t, cos t, sin
2t
, 0 ≤ t ≤ 2π.
(Hint: Observe that C lies on the surface
z = 2xy.)
part 1)
Find dy/dx by implicit differentiation.
3x^6+x^5y−2xy^6=8
dy/dx=
part 4)
A campground owner has 2000 meters of fencing. She wants to enclose a rectangular field bordering a lake, with no fencing needed along the lake: see the sketch.
a) Write an expression for the length of the field: 2000-x (this is correct)
b) Find the area of the field (length times width): -x^2+2000x (this is correct)
c) Find the value of x leading to the maximum area:
d)...
Problem 7. Consider the line integral Z C y sin x dx − cos x dy.
(Please show all work)
a. Evaluate the line integral, assuming C is the line segment
from (0, 1) to (π, −1).
b. Show that the vector field F = is conservative, and find a
potential function V (x, y).
c. Evaluate the line integral where C is any path from (π, −1)
to (0, 1).
Use implicit differentiation in each of the following problems
to find dy/dx. Then determine the equation of a tangent line at the
given point.
(a) y = xe^y , at (1/e, 1)
(b) sin x cos y = sin x + cos y, at (0, π/2).
Hint: One of the lines is vertical, so its derivative is
undefined at the given point. Recall that the equation of a
vertical line has the form x = a.