Differeutate (0) you in (6) y: (In (3x+4)² (c) use logarithne differentiation y (13x-4) (2223) (4x-1)²....
Systems of Equations: 3x + y = 6 2x-2y=4 Substitution: Elimination: Solve 1 equation for 1 variable. Find opposite coefficients for 1 variable. Rearrange. Multiply equation(s) by constant(s). Plug into 2nd equation Add equations together (lose 1 variable). Solve for the other variable. Solve for variable. Then plug answer back into an original equation to solve for the 2nd variable. y = 6 -- 3x solve 1" equation for y 6x +2y = 12 multiply 1" equation by 2 2x...
for the following function (5 Marks) dy 5. (b) Use implicit differentiation to find dx 3x* - 6 ln(2xy) = 7-5e24-sy dy 1. (b) Evaluate: lim r? + 4x -12 (3-12x +1 (5 Marks)
use laplace transform 4. x" + 4x' + 13x = te-t, x(0) = 0, x'(0) = 2.
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
Consider the function y=ln(2)(-4x+3)(2^3x-2x^2) 1. What is the general expression of the elasticity in terms of x? 2. What value does the elasticity actually have when x=4?
#4 Complete the squares. a) x2 + 4x - y - 12 = 0 for x b) 2x + y2 - 6y = 1 for y #5 Solve the system of equations sx - y = 11 a) 12x + y = 19 1-3x - 2y = 1 b) 16x + 4y = -2
Use the Laplace transform to solve initial value problems 4. x" + 4x' + 13x = te-t, x(0) = 0, x'(0) = 2.
cos x + cos 2x cos 3x+ cos 4x 0, is a) 3 c) 7 b) 5 d) 9 Let tan-1 y = tan, + tan-1 ( tan-1 (-Zr where |x| < + v/3 Then a value of y is 1-3z2 1-32 1 + 3z2 1+3 If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to tower, are 300 450 and 60 respectively then the ratio,...
3x+2 f(x) =( :) (x-> +1) Your problem: using the rules of differentiation, find the derivatives of the collowing: f)-(3442) fool(3x+2) (-5x + x + 1) - 2 1 =(-15x 10x" + (-2x = 2) =>15x410x5 - 2x = = 3x -3x- 27 (X)(3+0)-(3x+2)(1) x² g'=(x) =F12x15x4_2 = -5x6 xb * please check my work, if wrong, please write out correct solation! Chain Rule: When functions are composed, to take the derivative involves both the outside function and the inside...
Multiple Choice: 1. Simplify "1-2x-x+5x-3x2+15+x3 a) x3-4x2+3x -1 (b) x2-4x2 +3x +1 (c) x3-4x-3x +1 (d)+4x +3x +1 2. Expand "logly' x3 a) 2(Logly)+3logx)) ( (d) 2logl)+3loglv) (b) 3log(x) 2logly) (c) 6log(x)logly) 3. quals 5 (b) 55 (c) 64 (d) 10 a) 62