EBK CALCULUS: AN APPLIED APPROACH
10th Edition
ISBN: 8220101426222
Author: Larson
Publisher: CENGAGE L
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Chapter A3, Problem 51E
To determine
To calculate: The domain of the expression
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In Exercises 102–103, perform the indicated operations. Assume
that exponents represent whole numbers.
102. (x2n – 3x" + 5) + (4x2" – 3x" – 4) – (2x2 – 5x" – 3)
103. (y3n – 7y2n + 3) – (-3y3n – 2y2" – 1) + (6y3n – yn + 1)
104. From what polynomial must 4x? + 2x – 3 be subtracted to
obtain 5x? – 5x + 8?
Make Sense? In Exercises 135–138, determine whether each
statement makes sense or does not make sense, and explain your
reasoning.
135. I use the same ideas to multiply (V2 + 5) (V2 + 4) that I
did to find the binomial product (x + 5)(x + 4).
136. I used a special-product formula and simplified as follows:
(V2 + V5)? = 2 + 5 = 7.
137. In some cases when I multiply a square root expression and
its conjugate, the simplified product contains a radical.
138. I use the fact that 1 is the multiplicative identity to both
rationalize denominators and rewrite rational expressions
with a common denominator.
In Exercises 101–103, perform the indicated operations.
1
1
1
101.
x" – 1 x" + 1 x2" – 1
(1-X- -X )
(1 –
(1 –
102. (1 -
x + 1)
x + 2
x + 3
103. (x – y)-1 + (x – y)-2
Chapter A3 Solutions
EBK CALCULUS: AN APPLIED APPROACH
Ch. A3 - Checkpoint 1 Worked-out solution available at...Ch. A3 - Prob. 2CPCh. A3 - Prob. 3CPCh. A3 - Prob. 4CPCh. A3 - Prob. 5CPCh. A3 - Prob. 6CPCh. A3 - Prob. 7CPCh. A3 - Prob. 1ECh. A3 - Prob. 2ECh. A3 - Prob. 3E
Ch. A3 - Prob. 4ECh. A3 - Prob. 5ECh. A3 - Prob. 6ECh. A3 - Prob. 7ECh. A3 - Prob. 8ECh. A3 - Prob. 9ECh. A3 - Prob. 10ECh. A3 - Prob. 11ECh. A3 - Prob. 12ECh. A3 - Prob. 13ECh. A3 - Prob. 14ECh. A3 - Prob. 15ECh. A3 - Prob. 16ECh. A3 - Prob. 17ECh. A3 - Evaluating Expressions In Exercises 1-20, evaluate...Ch. A3 - Prob. 19ECh. A3 - Prob. 20ECh. A3 - Prob. 21ECh. A3 - Prob. 22ECh. A3 - Prob. 23ECh. A3 - Prob. 24ECh. A3 - Simplifying Expressions with Exponents In...Ch. A3 - Prob. 26ECh. A3 - Prob. 27ECh. A3 - Prob. 28ECh. A3 - Prob. 29ECh. A3 - Prob. 30ECh. A3 - Prob. 31ECh. A3 - Prob. 32ECh. A3 - Prob. 33ECh. A3 - Prob. 34ECh. A3 - Prob. 35ECh. A3 - Prob. 36ECh. A3 - Prob. 37ECh. A3 - Prob. 38ECh. A3 - Prob. 39ECh. A3 - Prob. 40ECh. A3 - Prob. 41ECh. A3 - Prob. 42ECh. A3 - Prob. 43ECh. A3 - Prob. 44ECh. A3 - Prob. 45ECh. A3 - Prob. 46ECh. A3 - Prob. 47ECh. A3 - Prob. 48ECh. A3 - Prob. 49ECh. A3 - Prob. 50ECh. A3 - Prob. 51ECh. A3 - Prob. 52ECh. A3 - Prob. 53ECh. A3 - Prob. 54ECh. A3 - Prob. 55ECh. A3 - Prob. 56ECh. A3 - Prob. 57ECh. A3 - Prob. 58E
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- Scientific Notation. In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation. 614arrow_forwardExercises 38–40 will help you prepare for the material covered in the first section of the next chapter. In Exercises 38-39, simplify each algebraic expression. 38. (-9x³ + 7x? - 5x + 3) + (13x + 2r? – &x – 6) 39. (7x3 – 8x? + 9x – 6) – (2x – 6x? – 3x + 9) 40. The figures show the graphs of two functions. y y 201 10- .... -20- flx) = x³ glx) = -0.3x + 4x + 2arrow_forwardRewriting an Expression In Exercises 51–54,rewrite the quadratic portion of the algebraic expressionas the sum or difference of two squares by completingthe square.arrow_forward
- In Exercises 33–37, simplify each exponential expression. 33. (-2r)(7x-10) 34. (-&rSy)(-5x?y*) -10xty 35. -40x-2y6 36. (4x-Sy?)-3 -6xy 37. -2 2x*y 3,,-4arrow_forwardFor Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples. • In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2). • Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5). To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that x + 4 = (x + 2i)(x – 2i). 115. а. х - 9 116. а. х? - 100 117. а. х - 64 b. x + 9 b. + 100 b. x + 64 118. а. х — 25 119. а. х— 3 120. а. х — 11 b. x + 25 b. x + 3 b. x + 11arrow_forwardIn Exercises 126–129, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 126. Once a GCF is factored from 6y – 19y + 10y“, the remaining trinomial factor is prime. 127. One factor of 8y² – 51y + 18 is 8y – 3. 128. We can immediately tell that 6x? – 11xy – 10y? is prime because 11 is a prime number and the polynomial contains two variables. 129. A factor of 12x2 – 19xy + 5y² is 4x – y.arrow_forward
- In Exercises 115–116, express each polynomial in standard form-that is, in descending powers of x. a. Write a polynomial that represents the area of the large rectangle. b. Write a polynomial that represents the area of the small, unshaded rectangle. c. Write a polynomial that represents the area of the shaded blue region. 115. -x + 9- -x +5- x + 3 x + 15 -x + 4- x + 2 116. x + 3 x + 1arrow_forwardIllustrate the Quotient Rule ?arrow_forwardIn Exercises 83–90, perform the indicated operation or operations. 83. (3x + 4y)? - (3x – 4y) 84. (5x + 2y) - (5x – 2y) 85. (5x – 7)(3x – 2) – (4x – 5)(6x – 1) 86. (3x + 5)(2x - 9) - (7x – 2)(x – 1) 87. (2x + 5)(2r - 5)(4x? + 25) 88. (3x + 4)(3x – 4)(9x² + 16) (2x – 7)5 89. (2x – 7) (5x – 3)6 90. (5x – 3)4arrow_forward
- Calculusarrow_forwardIn Exercises 133–136, factor each polynomial completely. Assume that any variable exponents represent whole numbers. 133. y + x + x + y 134. 36x2" – y2n 135. x* 3n 12n 136. 4x2" + 20x"y" + 25y2marrow_forwardSection 11.1 Rational Exponents Simplify each expression. (5n³)² · n-6 (64x)arrow_forward
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