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We already know the functions defined by y =c+a+f[b(x-d)] with the assumption that b>0. To see...
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see...
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin(-2x) as a function of 2x. y= (b) How is your answer to part (a) related to y = sin(2x)? O It is the negative of y = sin (2x). olt equals y = sin (2x). (c) Use an even-odd identity to write y = cos(...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
Establish the identity. 1 - sin 0 cos e + COS 0 1 - sin e...
Establish the identity. 1 - sin 0 cos e + COS 0 1 - sin e = 2 sec Write the left side of the expression with a common denominator. Do not expand the numerator. cos (1 - sin o) Expand and simplify the numerator by rewriting without any parentheses. + cos20 cos (1 - sin o) Apply an appropriate Pythagorean Identity to simplify the numerator of the expression from the previous step. cos (1 - sin o) (Do not...
Odd and Even Functions An even function has the property f(x) =f(-x). Consider the function f(x)...
Odd and Even Functions An even function has the property f(x) =f(-x). Consider the function f(x) Now, f (-a)-(-a)"-d f(a) An odd function has the property f(-x)-f(x). Consider the function f(x) Now, f (-a) = (-a)' =-a3 =-f(a) Declarative & Procedural Knowledge Comment on the meaning of the definitions of even and odd functions in term of transformations. (i) (ii) Show that functions of the formx) are even. bx2 +c Show, that f(x) = asin xis odd and g(x) =...
In class, we considered a box with walls at x = 0 and x = L. Now consider a box with width L but centered at x = 0, so that it extends from x = L/2 to x = L/2 as shown in the figure.
In class, we considered a box with walls at \(x=0\) and \(x=L\). Now consider a box with width \(L\) but centered at \(x=0\), so that it extends from \(x=-L / 2\) to \(x=L / 2\) as shown in the figure. Note that this box is symmetric about \(x=0 .\) (a) Consider possible wave functions of the form \(\psi(x)=A \sin k x\). Apply the boundary conditions at the wall to obtain the allowed energy levels.(b) Another set of possible wave functions...
MAC1114 - College Trigonometry - Project 2 Instructions: Either complete the project on separate or type...
MAC1114 - College Trigonometry - Project 2 Instructions: Either complete the project on separate or type your answers using MS Word. Label each of your problems clearly and in numerical order. Once your project is complete, save the document as a pdf file and upload your file using the Assignment link in Falcon Online, that is select Assignments and then select Project 1. If you are submitting a handwritten document, you must write NEATLY. If you are submitting a document...
In this exercise we consider the second order linear equation y" therefore has a power series solution in the form 4y = 0. This equation has an ordinary point at x = 0 and We learned how to easil...
In this exercise we consider the second order linear equation y" therefore has a power series solution in the form 4y = 0. This equation has an ordinary point at x = 0 and We learned how to easily solve problems like this in several different ways but here we want to consider the power series method (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn-2 for n - 2, 3, NOTE co...
THEOREM. Suppose that F(x, y) = (P(x, y), Q(x, y)) is a vector-valued function of two...
THEOREM. Suppose that F(x, y) = (P(x, y), Q(x, y)) is a vector-valued function of two variables and that the domain of P(x,y) and Q(x,y) is all of R2. Then it is possible to find a function f(x,y) satisfying Vf = F if and only if Py = Q. Instructions: Use this Theorem to test whether or not each of the following vector-valued functions F(x,y) has a function f(x, y) that satisfies VS = F (that is, if there is...
a) If f(0) = 5sec° 0 – sec°O + sec e Find: f'(0) b) If f(x)=...
a) If f(0) = 5sec° 0 – sec°O + sec e Find: f'(0) b) If f(x)= xe * + In 8x3 +In( cos x) -2x e Find: f'O
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A,...
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao
Consider the periodic function defined by 1
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin(-2x) as a function of 2x. y= (b) How is your answer to part (a) related to y = sin(2x)? O It is the negative of y = sin (2x). olt equals y = sin (2x). (c) Use an even-odd identity to write y = cos(...
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
Establish the identity. 1 - sin 0 cos e + COS 0 1 - sin e = 2 sec Write the left side of the expression with a common denominator. Do not expand the numerator. cos (1 - sin o) Expand and simplify the numerator by rewriting without any parentheses. + cos20 cos (1 - sin o) Apply an appropriate Pythagorean Identity to simplify the numerator of the expression from the previous step. cos (1 - sin o) (Do not...
Odd and Even Functions An even function has the property f(x) =f(-x). Consider the function f(x) Now, f (-a)-(-a)"-d f(a) An odd function has the property f(-x)-f(x). Consider the function f(x) Now, f (-a) = (-a)' =-a3 =-f(a) Declarative & Procedural Knowledge Comment on the meaning of the definitions of even and odd functions in term of transformations. (i) (ii) Show that functions of the formx) are even. bx2 +c Show, that f(x) = asin xis odd and g(x) =...
MAC1114 - College Trigonometry - Project 2 Instructions: Either complete the project on separate or type your answers using MS Word. Label each of your problems clearly and in numerical order. Once your project is complete, save the document as a pdf file and upload your file using the Assignment link in Falcon Online, that is select Assignments and then select Project 1. If you are submitting a handwritten document, you must write NEATLY. If you are submitting a document...
In this exercise we consider the second order linear equation y" therefore has a power series solution in the form 4y = 0. This equation has an ordinary point at x = 0 and We learned how to easily solve problems like this in several different ways but here we want to consider the power series method (1) Insert the formal power series into the differential equation and derive the recurrence relation Cn-2 for n - 2, 3, NOTE co...
THEOREM. Suppose that F(x, y) = (P(x, y), Q(x, y)) is a vector-valued function of two variables and that the domain of P(x,y) and Q(x,y) is all of R2. Then it is possible to find a function f(x,y) satisfying Vf = F if and only if Py = Q. Instructions: Use this Theorem to test whether or not each of the following vector-valued functions F(x,y) has a function f(x, y) that satisfies VS = F (that is, if there is...
a) If f(0) = 5sec° 0 – sec°O + sec e Find: f'(0) b) If f(x)= xe * + In 8x3 +In( cos x) -2x e Find: f'O
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao
Consider the periodic function defined by 1
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