Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11, Problem 47SP
To determine
To find: the largest and smallest value of the function
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4. Are the following functions cubic splines?
a. f(x) - x - 2x + 3, 0 sxs1,
= 2x - 3x2 + x + 2, 1sxs2.
b. f(x) = 5x - 3x + 1,0 sxs1,
- 2x + 6x? - 9x + 4, 1sxs2.
6. The domain of y = v1-x2 is
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;).
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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- 4. For a function f(x) = pe + qe¬¤ where p and q are non-negative real numbers such that p + q = 1, for what value of x does this function take its minimum value?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_forward18. Let A = = {W,Y, Z}, C = {r, V2, V5}. Find examples of two functions f: A→ B, and g : B → C, such that {1,2, 3}, B || (a) f is one-to-one, and yet g of is not.arrow_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_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_forward4. If f is a coordinate system on a line /, determine whether or not each of the following functions is a coordinate system on /. a. g(P) = f(P) - 10 b. h(P) = 10f(P) c. K(P) = 10 f(P) d. r(P) = f(P) + the square root of 10arrow_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_forwardFind minimum and maximum for the function 6 x + 4 y under conditions: x2 0; yz 0; -x+y s 12; x+ys 24; 2 x + 5 y s 80 5.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_forward6. A flying robot is programed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in x, y, and z are measured in meters and t in seconds. x(t) = 0.0560t* – 1.200t² + 2.300t + 0.3400 y(t) = 0.6700t3 – 1.570t² z(t) = 0.2200t³ (a) At t = 1.44 s, what angle does the robot's velocity vector, v, make with its acceleration vector, å? Osarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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