using the general power rule Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2...
3. Let X; - x2 + x3 = 0 for parts (a) and x + 3X2 = 0 2X - 2x2 + 3x3 =0 . (b) below: a) Find the determinant of b) Does the system of equations have a solution ? If yes, what is it?
Find the derivative of y with respect to x. y= In 1 + 2x X2 OA. -4-3x 2x OB. 4 – 3 x 2x(1 + xx) -4-3/ 2(1+) -4-377 2x(1+x) OD.
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
EXAMPLE 4 Then x2 + x-5 Let y = x3 + 6 2+x-5 y' - (x2 + x - - 5)( ++6 (x3 + 6)2 + 6 6)(2x + 1 +(x2+x - 5)( 3r? (x3 + 6) (+ 2x + 1 | ) - ( 374 +373 – 15r2 ) (x3 + 6)2 -2x3 +15x2 + 8x+4 (x3 + 5)2
13. 0/1.78 points | Previous Answers RogaCalcET3 10.6.052. My Note Use the power series for (1+x3)-1 and differentiation to find the power expansion for fx)-3X- 3x2 (x3 + 1)2 1 14. 0.46/1.86 points| Previous Answers RogaCalcET3 10.6.046. My Notes Ask Your Teacher Use the formula In(1 + x)- x- X23-*+.. for |x| <1 2 3 4 n-1 and your knowledge of alternating series to find the smallest N such that the partial sum Sy approximates In Confirm this using a...
Find the derivatives of the following functions (A) y=xt-x2 (B) y=x2 (C) y-3x3 + 4x -3 (D) y=x (F) f(x)- 100x100 (G) fx)- (H) f(x)=- 1-5r ) f(x)= (J f(x) - (x + 1)(x3 +5x + 2) (Requires quotient rule) 4+x For f(x) = 6x3, find f(x) and f"(x), and fm(x). For f(x)- 5x3 -3x2+x-20, find f(x), f"(x), and f""(x)
3. Use Cramer's rule to solve the following equation systems: (a) 8x1 - x2 = 16 (©) 4x + 3y - 2z=1 2x2 + 5x3 = 5 x + 2y = 6 2X1 + 3x3 = 7 3x + Z=4 (6) - X1 + 3x2 + 2x3 = 24 (d) -x + y +7= a X, + x3 = 6 x-y+z=b Sx2 - X+Y-7=C X3 = 8
8. Using Chain Power Rule a) ∫ (3X^2 + 4)^5(6X) dx b) ∫](2X+3)^1/2] 2dx c) ∫X^3](5X^4+11)^9 dx d ∫(5X^2(X^3-4)^1/2 dx e) ∫(2X^2-4X)^2(X-1) dx f) ∫(X^2-1)/(X^3-3X)^3 dx g) ∫(X^3+9)^3(3X^2) dx h) ∫[X^2-4X]/[X^3-6X^2+2]^1/2 dx
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
1. Find f(x) f(x) = 27 {rewrite first-leave answer as a radical) 3 +1 2. Find f'() 2. Find f'(x) f(x) = x {rewrite first; 3. Find f(x) f(x) = 21n(1+3x2) + 3e(4433) 4. Find f'(x) for f(x) = x2\n(x3+1) {Note: uses product rule f'g+g'f} dir dx 2x+1 f'g-g'ſ 5. Find {Note: uses quotient rule }