Essential Calculus: Early Transcendenta...
Publisher: Cengage Learning
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Solutions for Essential Calculus: Early Transcendentals
T Diagnostic Tests
1 Functions And Limits
3 Inverse Functions: Exponential, Logarithmic, And Inverse Trigonometric Functions
4 Applications Of Differentiation
6 Techniques Of Integration
7 Applications Of Integration
9 Parametric Equations And Polar Coordinates
10 Vectors And The Geometry Of Space
11 Partial Derivatives
12 Multiple Integrals
13 Vector Calculus
B Sigma Notation
C The Logarithm Defined As An Integral
Evaluate each expression without using a calculator. (a) (3)4 (b) 34 (c) 34 (d) 523521 (e) (23)2 (f)...
Simplify each expression. Write your answer without negative exponents. (3a3b3)(4ab2)2
Expand and simplify. 3(x + 6) + 4(2x − 5) (x + 3)(4x − 5) (2x + 3)2 (x + 2)3
Factor each expression. 4x2 − 25 2x2 + 5x − 12 x3 − 3x2 − 4x + 12 x4 + 27x 3x3/2 − 9x1/2 +...
Simplify the rational expression.
Rationalize the expression and simplify. (a) (b)
Rewrite by completing the square. x2 + x + 1 2x2 − 12x + 11
Solve the equation. (Find only the real solutions.) x + 5 = 14 −x x2 − x − 12 = 0 2x2 + 4x +1 =...
Solve each inequality. Write your answer using interval notation. −4 < 5 − 3x ≤ 17 x2 < 2x + 8 x(x −...
State whether each equation is true or false.
Find an equation for the line that passes through the point (2, 5) and (a) has slope 3 (b) is...
Find an equation for the circle that has center (1, 4) and passes through the point (3, 2).
Find the center and radius of the circle with equation x2 + y2 – 6x + 10y + 9 = 0.
Let A(−7, 4) and B(5, −12) be points in the plane. Find the slope of the line that contains A and...
Sketch the region in the xy-plane defined by the equation or inequalities. −1 ≤ y ≤ 3 | x | < 4 and...
The graph of a function f is given at the left. (a) State the value of f(1). (b) Estimate the value...
If f(x) = x3, evaluate the difference quotient f(2+h)f(2)h and simplify your answer.
Find the domain of the function. (a) f(x)=2x+1x2+x2 (b) g(x)=x3x2+1 (c) h(x)=4x+x21
How are graphs of the functions obtained from the graph of f? (a) y = f(x) (b) y = 2f(x) 1 (c) y =...
Without using a calculator, make a rough sketch of the graph. y = x3 y = (x + 1)3 y = (x − 2)3 +...
Let Evaluate f(−2) and f(1). Sketch the graph of f.
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...
Convert from degrees to radians. 300° −18°
Convert from radians to degrees. (a) 5/6 (b) 2
Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of...
Find the exact values. (a) tan(/3) (b) sin(7/6) (c) sec(5/3)
Express the lengths a and b in the figure in terms of θ. FIGURE FOR PROBLEM 5
If sinx=13 and secy=54, where x and y lie between 0 and /2, evaluate sin(x + y).
Prove the identities. tan θ sin θ + cos θ = sec θ
Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π.
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