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Write the first five terms of the geometric sequence defined recursively. Find the common ratio and...
Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the nth term of the sequence as a function of n. (nth term formula: An = a1(r)-1) 1 a1 = 625, ak 11 = 5 -ak aj = a2 a3 = 04 = Preview 05 Preview r = Preview an = Preview Find the 6th of the geometric sequence: {64a( – b), 32a( – 36), 16a( – 96), 8a( – 27b), ...} an...
plz help me analysis question! Thanks in advance 2. Let h : R-+ R be the smooth function given by h(z) g is as in Probl...
plz help me analysis question!
Thanks in advance
2. Let h : R-+ R be the smooth function given by h(z) g is as in Problem 1 g(z + 2g(2-x) for all r E R, where (a) Show that if a < -2 0 g(2) if -2< <-1 h(x) if 2 0 (b) Use part (d) of Proble 1 to show that for all E 0,9 in fact for all ,. Conclude that for all e 0,1 The functions from...
DIRECTIONS: Show all of your work and write your answer in the space provided. MODIFIED TRUE/FALSE:...
DIRECTIONS: Show all of your work and write your answer in the space provided. MODIFIED TRUE/FALSE: If the statment is true, write true in the blank. If it is false, replace the underlined word(s) with the word(s) that will make the statement true. 1. A series that tends toward a single number is called a divergent series. 2. A series is the product of the terms in a sequence. 3. A(n) alternating geometric sequence switches between positive and negative values....
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g...
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g(2)-3 realnumbers. The graph of its derivative, g'(z), g'(a) Also define the differentiable, odd function hz) on all real numbers. Some values of h(z) are given below 0 12 3 4 5 h(z 02-42 2 (a) Calculate each of the following quantities or, if there isn't enough information, explain why i. (g'(x) +2) dr i.h() da ii. (h'(z) +2z) dr iv. 8h(x) dr...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
Exercise 2. [10 pts] The floor and ceiling functions, denoted R-Z defined by and respectively, are...
Exercise 2. [10 pts] The floor and ceiling functions, denoted R-Z defined by and respectively, are functions Now define a function T : N → N by the recurrence T(1) = 1, T(n) = T (ln/2]) + T(r/2) for n > 2. Find a non-recursive formula for T(n), and prove that your formula is correct.
26. A sequence is defined recursively by the formula b, -4,4-2, with h -1 and b,...
26. A sequence is defined recursively by the formula b, -4,4-2, with h -1 and b, = 3. What is the value Show the work that leads to your answer. or 27. The recursive formula to describe a sequence is represented by -2 la=1+3a. Determine the first four terms of this sequence. Can this sequence be represented using an explicit geometric formula? Justify your answer. 28. A small jet has an airspeed (the rate in still air) of 300 mi/h....
Suppose that the functions g and h are defined as follows g (x)-x-2 h(x)-(r- 1)(r-3 (a)...
Suppose that the functions g and h are defined as follows g (x)-x-2 h(x)-(r- 1)(r-3 (a) Find (-4) (b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas. (b) Value(s) that are NOT in the domain of h :
# 4: For smooth complex valued functions f(x), g(z) defined for 0 < x inner product<f(x),g(x) > by 2π define the Hermitian Introduce the operator D(f() a)Show that <D(f(x),9()), D(g(x)) &...
# 4: For smooth complex valued functions f(x), g(z) defined for 0 < x inner product<f(x),g(x) > by 2π define the Hermitian Introduce the operator D(f() a)Show that <D(f(x),9()), D(g(x)) > if f b) For n and integer show that einz for 0-x-2n satisfi c) Show that for mメn both integers then < einz, enny-0, 0,警) (0)- ic boundary conditions. Also onormal and < einz, einz >-2T. θ, Call these last periodic boundary conditions for f(x), g(s), show that D(einz)...
a) A vector field F is called incompressible if div F = 0. Show that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is incompressible. b) Suppose that S is a closed surface (a boundary o...
a) A vector field F is called incompressible if div F = 0. Show
that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is
incompressible.
b) Suppose that S is a closed surface (a boundary of a solid in
three dimensional space) and that F is an incompressible vector
field. Show that the flux of F through S is 0.
c)Show that if f and g are defined on R3 and C is a closed curve
in R3 then...
Write the first five terms of the geometric sequence defined recursively. Find the common ratio and write the nth term of the sequence as a function of n. (nth term formula: An = a1(r)-1) 1 a1 = 625, ak 11 = 5 -ak aj = a2 a3 = 04 = Preview 05 Preview r = Preview an = Preview Find the 6th of the geometric sequence: {64a( – b), 32a( – 36), 16a( – 96), 8a( – 27b), ...} an...
plz help me analysis question!
Thanks in advance
2. Let h : R-+ R be the smooth function given by h(z) g is as in Problem 1 g(z + 2g(2-x) for all r E R, where (a) Show that if a < -2 0 g(2) if -2< <-1 h(x) if 2 0 (b) Use part (d) of Proble 1 to show that for all E 0,9 in fact for all ,. Conclude that for all e 0,1 The functions from...
DIRECTIONS: Show all of your work and write your answer in the space provided. MODIFIED TRUE/FALSE: If the statment is true, write true in the blank. If it is false, replace the underlined word(s) with the word(s) that will make the statement true. 1. A series that tends toward a single number is called a divergent series. 2. A series is the product of the terms in a sequence. 3. A(n) alternating geometric sequence switches between positive and negative values....
2. Problem 2 Let g(z) be a differentiable function defined on is shown below. Also suppose that g(2)-3 realnumbers. The graph of its derivative, g'(z), g'(a) Also define the differentiable, odd function hz) on all real numbers. Some values of h(z) are given below 0 12 3 4 5 h(z 02-42 2 (a) Calculate each of the following quantities or, if there isn't enough information, explain why i. (g'(x) +2) dr i.h() da ii. (h'(z) +2z) dr iv. 8h(x) dr...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
Exercise 2. [10 pts] The floor and ceiling functions, denoted R-Z defined by and respectively, are functions Now define a function T : N → N by the recurrence T(1) = 1, T(n) = T (ln/2]) + T(r/2) for n > 2. Find a non-recursive formula for T(n), and prove that your formula is correct.
26. A sequence is defined recursively by the formula b, -4,4-2, with h -1 and b, = 3. What is the value Show the work that leads to your answer. or 27. The recursive formula to describe a sequence is represented by -2 la=1+3a. Determine the first four terms of this sequence. Can this sequence be represented using an explicit geometric formula? Justify your answer. 28. A small jet has an airspeed (the rate in still air) of 300 mi/h....
Suppose that the functions g and h are defined as follows g (x)-x-2 h(x)-(r- 1)(r-3 (a) Find (-4) (b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas. (b) Value(s) that are NOT in the domain of h :
# 4: For smooth complex valued functions f(x), g(z) defined for 0 < x inner product<f(x),g(x) > by 2π define the Hermitian Introduce the operator D(f() a)Show that <D(f(x),9()), D(g(x)) > if f b) For n and integer show that einz for 0-x-2n satisfi c) Show that for mメn both integers then < einz, enny-0, 0,警) (0)- ic boundary conditions. Also onormal and < einz, einz >-2T. θ, Call these last periodic boundary conditions for f(x), g(s), show that D(einz)...
a) A vector field F is called incompressible if div F = 0. Show
that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is
incompressible.
b) Suppose that S is a closed surface (a boundary of a solid in
three dimensional space) and that F is an incompressible vector
field. Show that the flux of F through S is 0.
c)Show that if f and g are defined on R3 and C is a closed curve
in R3 then...
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