Calculus Answers

Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
u=ax+(1-a)y+b

Given that
ϕ
=
l
n
|
r
|
ϕ=ln|r|
such that r=xi+yj+zk find
▽
ϕ

Determine the directional derivative of
f
=
x
y
2
+
y
z
3
f=xy2+yz3
at the point (2, -1, 1) in the direction of vector i+2j+2k

Find the curl of
A
=
x
2
y
i
−
2
x
z
j
+
2
y
z
k
A=x2yi−2xzj+2yzk
at the point (1, 0, 2).

Find the unit outward drawn normal to the surface
(
x
−
1
)
2
+
y
2
+
(
z
+
2
)
2
(x−1)2+y2+(z+2)2
= 9 at the point (3, 1, -4)

Find the area bounded by the curve y=4x-x^2 and the line x=0 and y=4

Find an explicit rule for the nth term of the sequence.

2, -8, 32, -128, ...

Given the scalar defined by ∅(x,y,z) = 3x^2z - xy^2 + 5. find ∅ at the points(-1,-2,-3)
(a)12 (b)19 (c)19 (d)5

The gradient of the tangent drawn at any point on a curve is given by m= dy/dx =1 -4x. Determine the equation of the curve if it passes through point (-2,4).

The projection map defined on (R^2,d) where d is the usual metric is continuous.Is it true?