![[b] Find a formula for the following sum: S = 3+ 2x + 32 + 4x +...+ (m - 1)an-1 for any n e N, n >1 and any x ER.](http://img.homeworklib.com/questions/ad1f0b50-c4b4-11ea-838f-e9be104fd793.png?x-oss-process=image/resize,w_560)
Homework Answers
(c) Find a formula for the inverse of the function. 4x-1 ) f(x) _[3 marks] 2x+3...
(c) Find a formula for the inverse of the function. 4x-1 ) f(x) _[3 marks] 2x+3 (ii) f(x) = /10 - 3x [2 marks) 1+1 (111) g(x) = 1-e* [3 marks] Total: 25 marks!
(3) For the system modeled by with output defined as a) Find the system's transfer function(s)...
(3) For the system modeled by with output defined as a) Find the system's transfer function(s) E(t) +3z(t) +2x(t)-Sult) b) Find the system's pole(s) (if any) and zero(s) (if any) c) Find n(t →x) if u(t)-G 120) 0 t<0 e) Find the frequency response function corresponding to output y 1) Find steady-state ya(t) if u(t) 3sin(21)
Solve the following linear inequalities. Give answers in interval notation a) -2x+S>23 S-2x c) ts프>x or...
Solve the following linear inequalities. Give answers in interval notation a) -2x+S>23 S-2x c) ts프>x or 3x+621 d) 3x+ 3 S-3 and 4x +2>2 Find the slope-intercept form of the line which passes through the given points a) P(2, 3) Q(-6,0) b) P(4,7) 0(7.7)
cos x + cos 2x cos 3x+ cos 4x 0, is a) 3 c) 7 b)...
cos x + cos 2x cos 3x+ cos 4x 0, is a) 3 c) 7 b) 5 d) 9 Let tan-1 y = tan, + tan-1 ( tan-1 (-Zr where |x| < + v/3 Then a value of y is 1-3z2 1-32 1 + 3z2 1+3 If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to tower, are 300 450 and 60 respectively then the ratio,...
1 1 1 [3 marks] 32.. 1 (a) Find the sum to infinity of the series...
1 1 1 [3 marks] 32.. 1 (a) Find the sum to infinity of the series 2-3+ [3 marks] (b) Show that x+ 2x + 3x + ... + x = nx(n+1) (c) Show that Esin'(x) = sing if \sin xkl. [3 marks]
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6...
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6 = 2-5x a. b. x/m + x/n = 1 C 1/x = 3/m d. Sx/3 = 2 34. Find b if: x/(x+a) = 2/b a. b. v(x - b') =y 35. Solve the following Simultaneous linear equations and check in both equations: a) 3x+y=-4 x-2y 1 b) 5x+y=-8 2x-2y 4 Answer: x-1, y.3 36. Evaluate the expression below, if b-3 and c-2. 2bc'+(bc) Helpful...
13. S(3 – 2x – 4x²)(1+4x) dx 14. S Inx) dx =
13. S(3 – 2x – 4x²)(1+4x) dx 14. S Inx) dx =
Problem 25 please -Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e...
Problem 25 please
-Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e 22. W= Span(B),where B= ({x25, x5*, 5x)); f(x)--4x2 5x+9s5x-2(5x). 3 W Span(B), where B (Exsin(2x), xcos(2x), sin(2x), cos(2x)y): f(x) = 4x sin(2x) + 9x cos(20-5 sin(2x) + 8 cos(2x). 24, In Exercise 21 of Section 3.6, we constructed the matrix [D, of the derivative operator D on W- Span(B), where B e sin(bx), e" cos(bx)): Dls a a. Find [D 1g and [D'lg: Observe...
7. (Lesson 3.5) Let S(x)=-8x+16, if x53 [ax+b, if x>3. Find a and b such that...
7. (Lesson 3.5) Let S(x)=-8x+16, if x53 [ax+b, if x>3. Find a and b such that the function(x) is differentiable everywhere. (HINT: First use differentiability to find a. Then use continuity to find b.) M 8 . (Lesson 3.6) Memorize the following integration formulas, then practice using them. Power Rule: If n*-1, then ſx"dx = --***!+C Constant Multiple Rule: ſk. (x)=k[ /[x]cle Sum/Difference Rule: (x)£g(x)}!x = 5 /(x)det g(x) (b) f(6x–3Vx+dr = — (a) dr = — 9. (Lesson 3.6)...
Exercise 3.3: Nonlinear equations 1. Find the zeros of the following functions graphically: b) g\left(x\right)=2x^2-4x-16 4...
Exercise 3.3: Nonlinear equations 1. Find the zeros of the following functions graphically: b) g\left(x\right)=2x^2-4x-16 4 c) For the following function determine if x = 1 is a root: 5. Find the rational roots, if any, of the following: b) 8x^3+6x^2-3x-1=0 6. Find the equilibrium solution for each of the following models: a) Q_d=Q_s Q_d=3-P^2 Q_s=6P-4
(c) Find a formula for the inverse of the function. 4x-1 ) f(x) _[3 marks] 2x+3 (ii) f(x) = /10 - 3x [2 marks) 1+1 (111) g(x) = 1-e* [3 marks] Total: 25 marks!
(3) For the system modeled by with output defined as a) Find the system's transfer function(s) E(t) +3z(t) +2x(t)-Sult) b) Find the system's pole(s) (if any) and zero(s) (if any) c) Find n(t →x) if u(t)-G 120) 0 t<0 e) Find the frequency response function corresponding to output y 1) Find steady-state ya(t) if u(t) 3sin(21)
Solve the following linear inequalities. Give answers in interval notation a) -2x+S>23 S-2x c) ts프>x or 3x+621 d) 3x+ 3 S-3 and 4x +2>2 Find the slope-intercept form of the line which passes through the given points a) P(2, 3) Q(-6,0) b) P(4,7) 0(7.7)
cos x + cos 2x cos 3x+ cos 4x 0, is a) 3 c) 7 b) 5 d) 9 Let tan-1 y = tan, + tan-1 ( tan-1 (-Zr where |x| < + v/3 Then a value of y is 1-3z2 1-32 1 + 3z2 1+3 If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to tower, are 300 450 and 60 respectively then the ratio,...
1 1 1 [3 marks] 32.. 1 (a) Find the sum to infinity of the series 2-3+ [3 marks] (b) Show that x+ 2x + 3x + ... + x = nx(n+1) (c) Show that Esin'(x) = sing if \sin xkl. [3 marks]
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6 = 2-5x a. b. x/m + x/n = 1 C 1/x = 3/m d. Sx/3 = 2 34. Find b if: x/(x+a) = 2/b a. b. v(x - b') =y 35. Solve the following Simultaneous linear equations and check in both equations: a) 3x+y=-4 x-2y 1 b) 5x+y=-8 2x-2y 4 Answer: x-1, y.3 36. Evaluate the expression below, if b-3 and c-2. 2bc'+(bc) Helpful...
13. S(3 – 2x – 4x²)(1+4x) dx 14. S Inx) dx =
Problem 25 please
-Sesin(2x)-9ecos(2x). 21. W = Span(B), where Br(x2e-4x , xe®, e-4x); f(x)--5x2r" + 2e-4-1e 22. W= Span(B),where B= ({x25, x5*, 5x)); f(x)--4x2 5x+9s5x-2(5x). 3 W Span(B), where B (Exsin(2x), xcos(2x), sin(2x), cos(2x)y): f(x) = 4x sin(2x) + 9x cos(20-5 sin(2x) + 8 cos(2x). 24, In Exercise 21 of Section 3.6, we constructed the matrix [D, of the derivative operator D on W- Span(B), where B e sin(bx), e" cos(bx)): Dls a a. Find [D 1g and [D'lg: Observe...
7. (Lesson 3.5) Let S(x)=-8x+16, if x53 [ax+b, if x>3. Find a and b such that the function(x) is differentiable everywhere. (HINT: First use differentiability to find a. Then use continuity to find b.) M 8 . (Lesson 3.6) Memorize the following integration formulas, then practice using them. Power Rule: If n*-1, then ſx"dx = --***!+C Constant Multiple Rule: ſk. (x)=k[ /[x]cle Sum/Difference Rule: (x)£g(x)}!x = 5 /(x)det g(x) (b) f(6x–3Vx+dr = — (a) dr = — 9. (Lesson 3.6)...
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