Let f(x) = x3 + x. This is a one-to-one function. What is f(f(-2) + 3)...
Please give a detailed answer and explanation.
Question 2 Let f(x) =x+x3 for x e [0, π] . what coefficients of the Trigonometric Fourier Series of f(x) are zero? Which ones are non-zeros? Why? Let g (x) = cos (r) + sin (x*). What coefficients of the Trigonometric Fourier Series of g(x) are zero? Which ones are non-zeros? Why? (a) (b)
(15) The function f(x) = x3 +672 +3 is one-to-one on (-2,-4). Then (f-'Y(3) = A. does not exist 1 B. 6 C. 9 D. -3 E. 1 180 F. 36
what is all solutions of X3 of the system
( b) [5 marks] Let X= 2 and Let X2 = 5 be two solutions of the linear 3 system AX = B. Find all solutions X3 of this system, such that X3 # Xand X3 # X2 l]
(5) Let W denote the set of smooth functions f(2) in CⓇ such that f'(x) = -f(L). That is, W= {f() in C | F"(x) = -f(x)} In the previous worksheet, we showed that: • W is a subspace of Cº. . For all a and b, a sin(2) + b cos(x) is in W. (a) Show that (sin(x), cos(x)} are linearly independent. Hint: Set an arbitrary linear combination equal to 0, and show the coefficients must be 0. (b)...
For the function, f(x)#x3-7, determine whether it is one-to-one. If the function is one-toone, fnd a formula for the inverse Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ○ A. Yes, the function is one-to-one. The inverse function is f (x)- O B. No, the function is not one-to-one.
For the function, f(x)#x3-7, determine whether it is one-to-one. If the function is one-toone, fnd a formula for the inverse Select the...
1) Allow f(x) = x3, and g(x) = 2x. Determine f(g(1)). 2) Enter the formula for a sine function with an amplitude of 5, a period of 90 degrees, a shift of 45 degrees to the right and 3 units upwards. Determine the exact value of the expression sin (v) + cos (v) given that tan (v) = 7/3. 3) Solve the equations in the range 180≤x≤360 degrees. Answer with one decimal. a) tan (x) = 3.2 (I would like...
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f be its summation function n sin(nx) b) Show that f E C(R) and that 1 cos(nx) f'(x)= 2-1 c) Show that 「 f#072821) f(x)dx = k=0
Consider the series following series of functions ' sin(nx) 3 n-1 a) Show that the series is absolutely and uniformly convergent on the real axis. Let f...
Find the derivative of the following functions: (x2-1) f(x) = (x2 +1) f(x) = (x3 + 2x)3(4x + 5)2
Let f(x, y) = x²y + 5yº. At the point (1, -2), which one is incorrect about the behaviour of the function f: Select one: f(x, y) is decreasing at the rate of 4 units per unit increase in X. f(x, y) is increasing at the rate of 61 units per unit increase in y o the slope of the surface Z = f(x,y) in the y, direction is 61 f(x,y) is increasing at the rate of 4 units per...
Let W denote the set of smooth functions f(x) in CⓇ such that f"(x) = -f(x). That is, W = {f(x) in "S"(t) = -f(x)} . W is a subspace of C . For all a and b, a sin(x) + bcos(x) is in W. (a) Show that (sin(x), cos(x)} are linearly independent. Hint: Set an arbitrary linear combination equal to 0, and show the coefficients must be 0. (b) Let's say we knew that dim(W)=2. Show that (sin(x),cos(x)} is...