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Problem 5(4pts): For the functions f(x) and g(x) in problem 4, answer the following questions about...
9. (4pts) Consider the linear functions f(x) 6-x+3(x-4) and g (x)-3(x+)-5(+1). Solve f(x) g() algebraically, showing...
9. (4pts) Consider the linear functions f(x) 6-x+3(x-4) and g (x)-3(x+)-5(+1). Solve f(x) g() algebraically, showing all steps. (You may also check graphically) 10. 4pts) Test algebraically whether the function f(x)-4x- is even, odd, or neither even nor odd. Show your work. (You may also check your results graphically.) 11. (4pts) Determine whether the graph of y =-x' + 4x is symmetric with respect to the x-axis, the y-axis, and/or the origin. Use your graphing calculator make a sketch below...
5. Suppose that we have f(x)e. Use derivatives to answer the following questions. Solutions based on graphical or numerical work will receive no credit. (a) (4pts) Find f"(), the second deriv...
5. Suppose that we have f(x)e. Use derivatives to answer the following questions. Solutions based on graphical or numerical work will receive no credit. (a) (4pts) Find f"(), the second derivative of f(x) (b) (2 pts) Confirm that x =-1 is a critical point of f(x). (Evaluate f'(-1), and make a conclusion. (c) (4pts) Use the second derivative test to classify -1 as a local max. or a local min. If the second derivative test is inconclusive, then say so....
*9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point xo: (e) f,g : R-R given by f(x)and g(x) 1+2r ro0 (f) f, g : (...
*9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point xo: (e) f,g : R-R given by f(x)and g(x) 1+2r ro0 (f) f, g : (0, oo) → R given by f(r) = In(2) and g(z) = (z-1)3 + In(z): zo = 1. (g) f.g: (0, oo) -R given by f(x)-In(x) and g(x)-(x 1)200 +ln(x); ro 1 x-1)200
*9. For each of the following pairs of functions,...
Problem 10. Let f,g: [a,b] -R be Riemann integrable functions such that f(x) < g(x) for...
Problem 10. Let f,g: [a,b] -R be Riemann integrable functions such that f(x) < g(x) for all x E [a,b]. Prove that g(x)
Suppose that the functions f and g are defined as follows. f(x)=-4x+5 g(x) = 2x+1 Find...
Suppose that the functions f and g are defined as follows. f(x)=-4x+5 g(x) = 2x+1 Find f-g and . Then, give their domains using interval notation. 0 0 (-8)(x) = 0 0 .6 (0,0) [0,0] Domain off-g: 0 OVO (0,0] [0,0) Ø 00 -00 ()(w) = 0 5 ? Domain of I bo
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13 Differentiate. Let f and g be functions...
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
25 (4 comple The functions f and g are defined as f(x) = 8x - 5...
25 (4 comple The functions f and g are defined as f(x) = 8x - 5 and g(x) = - 6x?. a) Find the domain of f, g, f+g, f-g, fg, ff, and g' b) Find (f+g)(x), (f-g)(x), (fg)(x), (ff)(x), 0 (x), and (0)612 a) The domain offis I. (Type your answer in interval notation.) The domain of g is (Type your answer in interval notation.) The domain off+ 9 (Type your answer in interval notation.) The domain off-gis (Type...
9. Suppose that we are given the following information about the functions f,g and their deriva-...
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)
8. Suppose that we are given the following information about the functions f, g, h and...
8. Suppose that we are given the following information about the functions f, g, h and k and their derivatives; • f(1) = 3 • f'(1) = 2 • g(1) = 4 • g'(1) = -2 • h(1) = 9 . h'(1) = -1 k(1) = 10 • k'(1) = -3 (e) (5 points) Set F(x) = log2[f(x) + g(x)]. Compute F'(1). (f) (5 points) Set F(T) = log: [f(r)g(r)h(r)k(r)]. Compute F'(1).
9. (4pts) Consider the linear functions f(x) 6-x+3(x-4) and g (x)-3(x+)-5(+1). Solve f(x) g() algebraically, showing all steps. (You may also check graphically) 10. 4pts) Test algebraically whether the function f(x)-4x- is even, odd, or neither even nor odd. Show your work. (You may also check your results graphically.) 11. (4pts) Determine whether the graph of y =-x' + 4x is symmetric with respect to the x-axis, the y-axis, and/or the origin. Use your graphing calculator make a sketch below...
5. Suppose that we have f(x)e. Use derivatives to answer the following questions. Solutions based on graphical or numerical work will receive no credit. (a) (4pts) Find f"(), the second derivative of f(x) (b) (2 pts) Confirm that x =-1 is a critical point of f(x). (Evaluate f'(-1), and make a conclusion. (c) (4pts) Use the second derivative test to classify -1 as a local max. or a local min. If the second derivative test is inconclusive, then say so....
*9. For each of the following pairs of functions, determine the highest order of contact between the two functions at the indicated point xo: (e) f,g : R-R given by f(x)and g(x) 1+2r ro0 (f) f, g : (0, oo) → R given by f(r) = In(2) and g(z) = (z-1)3 + In(z): zo = 1. (g) f.g: (0, oo) -R given by f(x)-In(x) and g(x)-(x 1)200 +ln(x); ro 1 x-1)200
*9. For each of the following pairs of functions,...
Problem 10. Let f,g: [a,b] -R be Riemann integrable functions such that f(x) < g(x) for all x E [a,b]. Prove that g(x)
Suppose that the functions f and g are defined as follows. f(x)=-4x+5 g(x) = 2x+1 Find f-g and . Then, give their domains using interval notation. 0 0 (-8)(x) = 0 0 .6 (0,0) [0,0] Domain off-g: 0 OVO (0,0] [0,0) Ø 00 -00 ()(w) = 0 5 ? Domain of I bo
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
25 (4 comple The functions f and g are defined as f(x) = 8x - 5 and g(x) = - 6x?. a) Find the domain of f, g, f+g, f-g, fg, ff, and g' b) Find (f+g)(x), (f-g)(x), (fg)(x), (ff)(x), 0 (x), and (0)612 a) The domain offis I. (Type your answer in interval notation.) The domain of g is (Type your answer in interval notation.) The domain off+ 9 (Type your answer in interval notation.) The domain off-gis (Type...
9. Suppose that we are given the following information about the functions f,g and their deriva- tives and integrals; =4 f(0) = 0 • f(1) = • f'(1) = 2 g(0) = 5 g(1) = 4 • g'(1) =-2 So f(x)dx = 8 5* |(x)dx = 5 Sa f(x)dx = 11 S3 f (x)dx = 6 (d) (5 points) Evaluate Si f(x)dx. (e) (6 points) Evaluate ( f (.5.1 + 4)d.. (f) (6 points) Evaluate, (ثم) (g) (6 points) Evaluate,...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)
8. Suppose that we are given the following information about the functions f, g, h and k and their derivatives; • f(1) = 3 • f'(1) = 2 • g(1) = 4 • g'(1) = -2 • h(1) = 9 . h'(1) = -1 k(1) = 10 • k'(1) = -3 (e) (5 points) Set F(x) = log2[f(x) + g(x)]. Compute F'(1). (f) (5 points) Set F(T) = log: [f(r)g(r)h(r)k(r)]. Compute F'(1).
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