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- The derivative of y=em(sin 2x) is a) y = en(sin 2x) sin 2r b) y = en(sin 2x) cos 2x c) y' = 2 sin 2x d) y' = 2cos 2r29, given in terms of x and y for an Implicit Equation of y2+ x2 = siny + 4 RMI 18) Find y'= A) 2y/(2x - sin y) C) - 2x/(2y - cos y) B) 2x/(2y - cos y) D) - 2y /(2x - sin y) 19) Find an equation of the tangent line y = mx + b to an Implicit Equation of y2+ x2 = siny + 4 at the point (2, 0). A) y = - 2x +4 B) y = 2 x- 4 C) y = - 4x + 6 D) y = 4x - 8 1.5 20) Find (e sin x) dx = by Using TI-Calculator. A) 0. 412 B) 0. 698 C) 1. 573 D) 2. 912 2Solve Q5
- Q1) Show that: (a) (1+x)° =1+6x (b) (cosx) = -sinx dxIf x*y" + xy' + (x? -)y=D x >0 ,V1=x 2sinx and y = y,v. Which of the following equations satisfied by v Select one: a. (x 2 sinx)v" + (2x 2 cosx)v' = 0 b. (x 2sinx)v" +(2x 2 cosx)v=0 C. (x2sinx)v" + (2x cosx – xsinx + x2 sinx)v' = 0 cosx - x 2 sinx + x 2 sinx)v' = 0 d. (x 2 sinx)v" +(2x2 cosx)v' =03. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c) g(x) = -2 csc 7x + 8 sin 3x + 12 tan 2x d) y = (2x³ + 5x + 4 cos x)* e) f (0) = 2 tan(sin( 80))
- d2/dx2(1/x + cosx sinx)= A. -2/x3-2cosxsinx B. 2/x3-4cosxsinx C. 2/x3-2cosxsinx D. 2/x3 E. -2/x3+4cosxsinxI. Functions and Limits 1) If f(x) = x2 – x + 3, find f(-5y) and f(x³) x2-1 2) lim x-1 x2+3x-4 3) lim ) (y3-13y+12 y-3 \y3-14y+15. II. Derivatives 1) x = 2tvT + 2) v = (z* – 2z + 1). 3) f(x) = cos" (tan³(sin²(x³))) 4) f(x) = sec-'(1+ x²) 5) z = ecos(2x) 1911 BAGUIO CL 6) R = 74x-x² 7) f(x) = 7 log;(x5 – 9x) III. Implicit Differentiation Find y' by implicit differentiation. 1) x²y° = 2 2) = 4 3) 1= x* + 5y3 4) 8х — у? %3 3+3x2 B) Find dy/dx if : **")) (y)² = sin5 (cos³(
- sec(2) tan(2) – 1 dz 3.Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A (a,+a,²+a,t+a,)cos(xt) B - a t+a) cos (at) © (a,12+a,1+a,)² cos (xt) D(a,r²+a,t+a) cos(xt) +1(b,t²+b,t+b,) sin (xt) E (a,r²+a,t+a) cos (t) + (b,ť²+ b,t+b,) sin ( xt)2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin (0-a)