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(2.2) Let a be a real number with 1<a< 2. Put f(x) = Q +r 1+2 (a) Show that f maps (1, 0) into (1, 0). (b) Show that f is a contraction on [1, ) and find its fixed point.
1. Find the area between the graph x(t)=t^2, y(t)=t^2 + 2 and
the x-axis when 0 is less than or equal to t and t is less than or
equal to 4.
2. Find the surface area when the curve, x(t)=e^t + e^-t; y(t)=5
- 2t with 0 less than +t which is less than or equal to 3 and
rotation about the x-axis.
Please answer both problems if possible with work. Thank you in
advance.
1. Find the area...
12. Find all solutions with 0 <I<27: sec r = -2 13. Find all real solutions: sin r 2 14. Find all real solutions: 3 tan (3x) + 1 = 0
Real analysis. Please solve all questions
thank you
1. Let h be a positive real number, a <c< d < b and let Sh c< x <d, J() = 1 0 r < c, x > d (a) Using the definition only, find ſº f(x)dx. In fact, given e > 0, you should find an explicit d > 0) which works in the definition. (b) For a given partition P of [a, b], find a good upper bound on S(P)...
10 x(t) = { 1-0. 50.4Sts0.4 0 3.6 < t-0.4 A signal x (t) is defined as; (i) Dn (ii) Do (i) To (iv) ω。 (v) Sketch ID, 1 vs nu.。 (vi) Sketch <D (0) vs nw (vi Power of x(t) To implement Fourier Series 4.5 3.5 2.5 1.5 0.5 0 -2 (sec)
For all parts of this problem, let z(t) be the signal shown below. (Note that x(t) is defined by: x(t) = 3 - t for 0 <t <3; (t) = 0, otherwise.) 3 x(t) to i à (a) (6 points) Find the values of: (i) ſo r(t)8(t – 1)dt (ii) x(t)(t – 1)dt. (b) (6 points) Plot the signal y(t) defined by y(t) = x(r – 2)8(t – r)dr. (c) (6 points) Find the energy in x(t). (d) (7 points)...
3. Let X has the following pdf: {. -1 <1 fx(a) otherwise 1. Find the pdf of U X2. 2. Find the pdf of W X
(d) (4 points) Let T : R² + Rº be the transformation that rotates any vector 90 degrees counterclockwise. Let A be the standard matrix for T. Is A diagonalizable over R? What about over C? (e) (3 points) Let T : R4 → R4 be given by T(x) = Ax, A = 3 -1 7 12 0 0 0 4 0 0 5 4 0 4 2 1 Is E Im(T)? 3 (f) (9 points) Let U be a...
Let X be a random variable satisfying P(-1 X 1) = 0.3, P(X = 1.5) = 0.1, P(1.5 X P(3 X 7.4) 0.3, P(X 10)0.2 2) = 0.2 Find (i) P(X 2 1.3) (ii) P(X 2.3) ii P(1.5< X 2) (iv) P(1.5 3X 38)
let X be s random nareprion if x <0 > 0 (a) Let M= {X > 1). Find Fx( M)