Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Question (7):
![1. Find the tangent vector to the curve
6t
r(t) = [t³ – t,;
(2t + 1)2]
t+
at t = 1.
2. Find the length of the curve r(t)
0<t< 2n.
e'i + e' sin 2tj + e' cos 2tk,
3. Find a vector function that satisfies the conditions
r"(t) = 12ti – 31-/2j+2k,
r'(1) = j, r(1) = 2i – k.
4. Using the chain rule, find the following
A. 4, if z = u*v?w² and u = t³, v = 3t – 6, and w = t² +1.
B. and , if z = (x² + y²)8/2, and r = e=" sin v, y = e=" cos v.
5. Let f(r, y) = ce" + cos(ry) and P : (2,0).
A. Find the directional derivative of f at P in the direction v = 31 – 4j.
B. Find the direction of maximum increase of f at the point P.
6. Let f(x, y, z) = e* cosh y + z and P : (-1,0,0). Find the derivative
of f at the point P in the direction of v = i+ 2j+2k.
7. If f is a scalar field and v = [v1, v2, v3] is a vector field, show that
div(fv) = fdiv(v) + v • V(f).
%3D
8. Find div(v), if v is given by
v = (r? + y? + 22)--1, -y, -2].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b91b33a-b8ee-45b9-8e3d-b73ef2b7217b%2F650198b0-1f8d-4051-aa4e-64541aee3e33%2Fos0fcp6_processed.png&w=3840&q=75)
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