For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality 2 x x − 4 + 7 = 2 x 2 − 3 x + 5 − 2 + x
For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality 2 x x − 4 + 7 = 2 x 2 − 3 x + 5 − 2 + x
Solution Summary: The author explains that the linear equation is x=2 and the solution sets to the inequalities in interval notation.
a. Identify the type of equation or inequality (some may fit more than one category).
b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible.
• Linear equation or inequality
• Quadratic equation
• Rational equation
• Absolute value equation or inequality
• Radical equation
• Equation in quadratic form
• Polynomial equation
degree
>
2
• Compound inequality
2
x
x
−
4
+
7
=
2
x
2
−
3
x
+
5
−
2
+
x
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
College Algebra with Modeling & Visualization (5th Edition)
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