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When f(x) = 3x² + 2x +ă find the rate of change by finding hange by...
4. (a) Find the average rate of change of f(x) = 3x” – 2x+3 on [-2, 1]. (b) Write the equation of the secant line containing the points (-2, f(-2) and (1, f(1)).
Use Gaussian elimination to find the complete solution to each system (X-3y + z = 1 -2x + y + 3z =-7 x-4y + 2z = 0 A ((2t + 4, t + 1, t)h 0-B. {(2t + 5, t+2,t)) OC. (1t + 3, t + 2, t) D. ((3t 3, t+ 1, t))
Find the unit tangent vector to the curve defined by T F(t) = (2 cos(t), 2 sin(t), – 4 sin?(t)) at t 6 1 (6) (-1/4 + sqrt(3)*, sqrt(3)/4 + 11 * , sqrt(3)/2 -1t * Preview + 3t = undefined. Preview 4 ✓3 4 V3 + 1t = undefined. Preview 1t = undefined. 2
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
(write After use Laplace Transform to transform the following initial value problem x" + 3x' + 2x=2e-t, x(O) = x'(0)=0, you should get X(s)= S-2 fraction as (S-2)/(S-4)(s+6) for (s-4)(3+6) -). Then, find x(t) = L-2(x(s)= 5 (write 5/6 by 6 -3t e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
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...
Given that f(x) = 3x + 1 g(x) = 5x - 8 and h(x) = 2x – 1 3 Find:- i) f(-4) = ii) g[h(5)] = iii) f[g(3)] = iv) g[h(x)] = vi) h-1(7) =
Find an antiderivative of the function f(x) = 2x® (3x? +4)? What is a possible antiderivative of the given function? O A. F(x) = 6 (3x® + 4) 3 OB. F(x) = (3x® + 4) 3 OC. F(x) = (3x +4) 3 OD. F(x) = § (3x?+4) 3
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...
Question 7 (3 points) If f(x) = 2x - 7, find: a. f(3x +2) b.f-?x)