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Problem 1ADT:

Evaluate each expression without using a calculator. (a) (3)4 (b) 34 (c) 34 (d) 523521 (e) (23)2 (f)...

Problem 2ADT:

Simplify each expression. Write your answer without negative exponents. (a) 20032 (b) (3a3b3)(4ab2)2...

Problem 3ADT:

Expand and simplify. (a) 3(x + 6) + 4(2x 5) (b) (x + 3)(4x 5) (c) (a+b)(ab) (d) (2x + 3)2 (e) (x +...

Problem 4ADT:

Factor each expression. (a) 4x2 25 (b) 2x2 + 5x 12 (c) x3 3x2 4x + 12 (d) x4 + 27x (e) 3x3/2 ...

Problem 5ADT:

Simplify the rational expression. (a) x2+3x+2x2x2 (b) 2x2x1x29x+32x+1 (c) x2x24x+1x+2 (d) yxxy1y1x

Problem 8ADT:

Solve the equation. (Find only the real solutions.) (a) x + 5 = 14 12x (b) 2xx+1=2x1x (c) x2 x 12...

Problem 9ADT:

Solve each inequality. Write your answer using interval notation. (a) 4 5 3x 17 (b) x2 LT; 2x + 8...

Problem 10ADT:

State whether each equation is true or false. (a) (p+q)2=p2+q2 (b) ab=ab (c) a2+b2=a+b (d) 1+TCC=1+T...

Problem 1BDT:

Find an equation for the line that passes through the point (2, 5) and (a) has slope 3 (b) is...

Problem 2BDT:

Find an equation for the circle that has center (1, 4) and passes through the point (3, 2).

Problem 4BDT:

Let A(7, 4) and B(5, 12) be points in the plane. (a) Find the slope of the line that contains A and...

Problem 5BDT:

Sketch the region in the xy-plane defined by the equation or inequalities. (a) 1 y 3 (b) | x | 4...

Problem 1CDT:

The graph of a function f is given at the left. (a) State the value of f(1). (b) Estimate the value...

Problem 4CDT:

How are graphs of the functions obtained from the graph of f? (a) y = f(x) (b) y = 2f(x) 1 (c) y =...

Problem 5CDT:

Without using a calculator, make a rough sketch of the graph. (a) y = x3 (b) y = (x + 1)3 (c) y = (x...

Problem 7CDT:

If f(x) = x2 + 2x 1 and g(x) = 2x 3, find each of the following functions. (a) f g (b) g f (c) g...

Problem 1DDT:

Convert from degrees to radians. (a) 300 (b) 18

Problem 2DDT:

Convert from radians to degrees. (a) 5/6 (b) 2

Problem 3DDT:

Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30.

Problem 8DDT:

Find all values of x such that sin 2x = sin x and 0 x 2.

1. FUNCTIONS AND LIMITS. Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. 2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. 3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. 5. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. 6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations. 8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. 10. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. 11. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Lagrange Multipliers. 12. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals. 13. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. The Divergence Theorem. Appendix A. Trigonometry. Appendix B. Proofs. Appendix C. Sigma Notation. Appendix D. The Logarithm Defined as an Integral

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Evaluate each expression without using a calculator. (a) (3)4 (b) 34 (c) 34 (d) 523521 (e) (23)2 (f)...(a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...Write an expression for the slope of the tangent line to the curve y = f(x) at the point (a, f(a)).(a) What is a one-to-one function? How can you tell if a function is one-to-one by looking at its...Explain the difference between an absolute maximum and a local maximum. Illustrate with a sketch.(a) Write an expression for a Riemann sum of a function f. Explain the meaning of the notation that...Stale the rule for integration by parts. In practice, how do you use it?(a) Draw two typical curves y = f(x) and y = g(x), where f(x) g(x) for a x b. Show how to...(a) What is a convergent sequence? (b) What is a convergent series? (c) What does limnan= 3 mean?...

(a) What is a parametric curve? (b) How do you sketch a parametric curve?What is the difference between a vector and a scalar?(a) What is a function of two variables? (b) Describe three methods for visualizing a function of...Suppose f is a continuous function defined on a rectangle R = [a, b] [c, d]. (a) Write an...What is a vector field? Give three examples that have physical meaning.Convert from degrees to radians. 210Write the sum in expanded form. 1. i=15i(a) By comparing areas, show that 13ln1.5512 (b) Use the Midpoint Rule with n = 10 to estimate ln...

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