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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Sometimes a derivative contains negative exponents, andsimplification requires that all exponents be positive.Write each of the expressions in Exercises 46–49 withoutnegative exponents.arrow_forwardThis Simplification of the expression below, where u, v, and w denotesuitable positive realy numbers log(uv/w)+log(uw/v)+log(vw/u)-log(uvw) is equal to zero (0).Explain what property makes the situation so.arrow_forwardShow that h(x)arrow_forward
- Show that x + is increasing on [1, 0).arrow_forwardSolve 2)Realize Roll's theorem of the function f(x) = x + 1/x on [1/2, 2]. 3)Realize Mean Value theorem of the function f(x) = x + 1/x on [1/2, 3].arrow_forwardWrite a delta - epsilon proof that shows that the function f(x) = 3x – 5 is continuous at x =arrow_forward
- Each of Exercises 15–30 gives a function f(x) and numbers L, c, and ɛ > 0. In each case, find an open interval about c on which the inequal- ity |f(x) – L| 0 such that for all x satisfying 0 0, L= 2m, c = 2, — тх, ɛ = 0.03 28. f(x) = mx, ɛ = c > 0 L = 3m, c = 3, m > 0, L = (m/2) + b, 29. f(x) c = 1/2, m> 0, ɛ = c > 0 = mx + b, 30. f(x) 3D тх + b, m> 0, L%3Dm+ b, с %3D 1, &%3D 0.05arrow_forwardAnswer the following questions about the functions whose derivatives are given in Exercises 1–5: a. What are the critical points of ƒ? b. On what open intervals is ƒ increasing or decreasing? c. At what points, if any, does ƒ assume local maximum and minimum values? 1. ƒ′(x) = x(x - 1) 2. ƒ′(x) = (x - 1)2(x + 2) 3. ƒ′(x) = (x - 1)(x + 2) 4. ƒ′(x) = (x - 1)2(x + 2)2 5. ƒ′(x) = (x - 1)e-xarrow_forwardLet h(x)arrow_forward
- In Exercises 1–4, use finite approximations to estimate the area under the graph of the function using a. a lower sum with two rectangles of equal width. b. a lower sum with four rectangles of equal width. c. an upper sum with two rectangles of equal width. d. an upper sum with four rectangles of equal width. 1. ƒ(x) = x2 between x = 0 and x = 1. 2. ƒ(x) = x3 between x = 0 and x = 1. 3. ƒ(x) = 1/x between x = 1 and x = 5. 4. ƒ(x) = 4 - x2 between x = -2 and x = 2.arrow_forwardIn Exercises 27–32, use a graphingutility to graph the function on the closed interval [a, b].Determine whether Rolle’s Theorem can be applied to f on theinterval and, if so, find all values of c in the open interval (a, b)such that f '(c= ' 0.) f(x)=|x|-1,[-1,1]arrow_forwardfind a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4, 5]arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage