Find (and prove) a general formula for the intergral a^(bx) cos(cx)dx , for any constants a,b,c
Find (and prove) a general formula for the intergral a^(bx) cos(cx)dx , for any constants a,b,c
Find dy/dx of the next relations Sol: y ylx 1 1-Cx C 2) 1+cx y' (1+cx1-cx a+bx ab 3) y= In Va-bx y's a2-b'x 4) y= atan (t); x = bcor (t) 6) x+2 7) y = 2v+ 45; donde v 52., W sec X 8)4x+3 8xy+e -e+ 8cos[tan(y)] = 0 arcsec (); x = elog2 (Int) 9) y 10) y sen[tan(x )] 11) y = cos[sen' (x)] cot + 4 12) y 13) y = [sec'(secx))P 14) y [Beae...
Problem 3. Let X be a discrete random variable, gx) - a+ bX+ cX, and let a. b, c be constants. Prove, using the definition of expectation of a function of a random variable, namely , that E(a + bX + cx?) = a + bE(X) + cE(X2)
Evaluate the following integral using residues: I = { cos(bx)-cos(ax) dx. x2 Let a and b: real constants such that a > b>0. Note: cos(bz)-cos(az) is well-behaved along the real axis (singularity at z = 0 is removable), ejbz-ejaz has a pole at the origin. Make sure to handle this point correctly 22
Evaluate the following integral using residues: cos(bx)-cos(ax) I = dx. x2 Let a and b: real constants such that a > b >0. Note: cos(bz)-cos(az) has a singularity at z = 0 is removable, z2 ejbz-ejaz has a pole at the origin. Make sure to handle this point correctly 22
parameter values (2 , 2 , 2 ,4 ) Minimize f (X , X)-X,-AX2+ bx 12+ Cx x2+ dx , 2 2 Use any programing language of your preference .Use constant lambda . Run optimization for three different starting points . Draw chart Optimality gap vs iterations . Minimize f (X X2)-X-AX2 + bx 2+ cx x 2+ . Use any programing language of your preference .Use constant lambda . Run optimization for three different starting points . Draw chart...
b. do cos(bx) red 200 on Select one: a. In |1 – cos(bx)| + C b. - csc(bx) – cot(bx) + C In |1 – cos(bx) +C sin(bx) d. bx – In sec(bx) + tan(bx) + C C.
Using reduction formula ***** 13. Evaluate, S sin 5x cos x dx. Also prove that, 53.4 sin mx cos nx dx = 0
Consider the the transformation T: P^2 -> T^2 defined by T(a+bx+cx^2) = (a+b, b-c). Find the kernel of T. Give 2 examples of vectors in the kernel.
Find the intergral St-st-tox) dx a) 2ln (x1 - 25 6 6x t6 6xxt C.) 2 ln/x/+25 3 3 2 +30 6x to | b.) se FC
13. Evaluate, S sin 5x cos x dx. Also prove that, 52" sin mx cos nx dx = 0 Using reduction formula *****