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Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Question
Chapter 11, Problem 47SP
To determine
To find: the largest and smallest value of the function
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Chapter 11 Solutions
Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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- 8. Decide which of the following sets are linearly independent in R". Justify your answer in each case. (a) X₁ = = {(1,0), (0, 1)} ℃R² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} ℃ R² (d) X4 = {(1,0), (0, 1), (1, 1)} C R² (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} CR³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (g) X7 = {(0,0,0), (0, 1, 0), (1, 1, 1), (–1, 0, 1)} ℃ R³ (h) X8 = {(0, 1,0), (1, 1, 1)} C R³ (i) X9 = {(4, 3, 0, 0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} ℃ R4 (j) X10 = {(1, 2, 0, 0), (0, 2, 3, 0), (0, 0, −1, 1)} ℃ Rª 9. Decide, for the sets X; above, for which i, j = {1, 2, ..., 10}, span(X₂) = span(X;).arrow_forward5. For each of the following assertions, first state whether it is true or false. Then, provide full support for your statement by using theorems, definitions and/or examples where applicable. No marks will be awarded for unsupported statements. (a) The function f(x,y, z) = 1 + 3z + x2 is a linear function. ry (b) Given that the function g(u, v) is an onto function, if f(g(u, v)) = h(u, v), then it logically follows that h(u, v) is always onto. (c) f(x) = x* is a one-to-one function on the subset of its domain where (-5arrow_forward8. Decide which of the following sets are linearly independent in R". Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} ℃ R² (b) X₂ = {(1,0), (2,0)} ℃ R² (c) X3 = {(-1,0), (0, 0)} CR² 2 (d) X₁ = {(1,0), (0, 1), (1, 1)} ℃ R² C (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} ℃ R³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (h) Xs = {(0, 1, 0), (1, 1, 1)} ℃ R³ 8 (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} ℃ R4 (j) X10 = {(1, 2, 0, 0), (0, 2, 3, 0), (0, 0, −1, 1)} ℃ Rªarrow_forward. Let ƒ(x) = (x² - 4)³. Do the following. (a) Find the maximum value and the minimum value of f on the interval [-1,3]. (b) For what value of c such that -1 ≤ c ≤ 3 does f attain its maximum value?arrow_forwardI have the following example: "For the function f : A = {a, b, c, d, e} → B = {1, 2,..., 6} defined in Example 10.2 byf = {(a, 3), (b, 5), (c, 2), (d, 3), (e, 6)},it follows that f −1(3) = {a, d}, f −1({1, 3}) = {a, d}, f −1(4) = ∅ and f −1(B) = A." How does f −1({1, 3}) = {a, d}, looking at f I dont see 1?arrow_forward8*. For each of the following functions, determine which, if any, of the following conditions the func- tion satisfies: concavity, strict concavity, convexity, strict convexity. (Use whatever technique is most appropriate for each case.) f(x, y) = x + y; f(x,y) = x+y-e² - e²+y; f(x, y, z) = x² + y² + 32² - xy + 2xz+yz.arrow_forward2. Let f be a continuous function defined on a closed, bounded interval I = [a, 6]. Assume that f is one-to-one. Let m (M, respectively) be the minimum (maximum, respectively) of f. Then by problem 1, we know that either f(a) = m and f(b) = M; or f(a) = M and f(b) = m. If f(a) monotone increasing. If f(a) = M and f(a) monotone decreasing. %3D %3D = m and f(b) = M, then show that f is strictly = m, then show that f is strictly %3D Hint: you need to use the Intermediate Value Theorem and argue by contradition. Remark: Problem 2 basically says the only way for a continuous func- tion to be one-to-one is to be strictly monotone. In other words, only strictly monotone continuous functions can have inverse. This is actually a Theorem in our text.arrow_forward13. Let S = {x eR :x20 and 2| Vx - 31 + Vx(Vx - 6) + 6 = 0. Then, S (a) is an empty set (b) contains exactly one element (c) contains exactly two elements (d) contains exactly four elementsarrow_forward1. This two part question asks you to determine whether a given map represents a function. (a) Determine whether f: QxQ→Q, given by is a function. f(a/b, c/d) = (a + c)/(b + d) f(², ²) = (a + c) (b+d) (b) Determine whether f: Q→ Z, given by is a function. f(a/b) = (a + b)(a - b)arrow_forwardQuestion 4arrow_forward6. Compute fryx (1,–3) and fyxy (1, -3) for f(x,y) = (x + y)*.arrow_forward2. Suppose a 4D space exists for variables a, b, c, and d, where a is a function of b, c, and d, then, the correct expression for finding the partial derivative of a with respect to b is (da/ab)..arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
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Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Double and Triple Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=UubU3U2C8WM;License: Standard YouTube License, CC-BY