Suppose that f(2) = -3, 9(2) = 4, f'(2) = -5, and g(2) = 1. Find h'(2). (a) h(x) = 3f(x) - 2g(x) h'(2) h(x) = f(x)g(x) (b) h'(2) (c) h(x) = f(x) g(x) h'(2) (d) h(x) g(x) 1 + f(x) h'(2)
Problem 4: If h(x) = f(g(x)) where f(-3) = 8, f'(-2) = 4, f'(5) = 3, 9(5) = -2 and 8'(5) = 6 find (5).
If z = f(x,y), where f is differentiable, and x = g(t) y = hết) g(3) = 2 h(3) = 7 g'(3) = 5 h'(3) = -4 fx(2,7) = 6 fy(2,7) = -8 Find dz/dt when t = 3.
Question 2 Find the indicated function value. Find f(-4) when f (x) 2² +4 23 62 O-2/7 0-5/16 0 - 1/2 O-2/5 Question 3 BILI SUULILULUI NV, O Question 5 3 pts Find the indicated function value: f(3) = 5 - 8a, g(x) = -3x + 8. Find (f + 9) (x) - 3x + 5 - 5x + 13 0 - 11x + 13 2x Question 6 3 pts Find the composition of functions: f(x) 70? + 4x, g(x)...
Find faults in the following arguments, with brief explanations: (a) First faulty argument: 2(2) (3x) F(x) 3 (3) F(a) (4) F(a)→G(a) 1,3 (5) G(a) 1,3 (6) (Vr) G(x) 1,2 (7) (Vr) G(x) 3,4 MP 2,3,6 3 E (b) Second faulty argument: (1) (yz)(33) H(z, y) 1 (2) y) H(a, y) (3) (4) 5(5) 4.5 (6) 4.5 (7) (3) H(by) H(a, b) H(b, a) H (a, b) ЛНФа) (3y)(H(a,y) ΛΗ(y, a)) 4,5 л! 6ヨ1 Now find models to demonstrate that the...
Evaluate. If fx) - x-5 and glx) x-1, evaluate (f + g)(2) a) 8 b) 10 c) o d) -2
Evaluate the following f(x)=x2-1 and g(x) = 3x +5. :a. f(-3) b. g(-2) c. f(0) d. g(5) 2. Find the x and y intercepts of the following functions: a) f(x) = x2 - 5x + 6 = 0b) h(x) = -2x + 20
3) [8 marks] Find fog and go f, where fx) -x+2 and glx) x+3, are functions from R to R. 4) [9 marks] Consider the proposed function,f: A x B x C ? D, as defined in the following table, where A B-C-D 0,1 Input Output ABC? D 1 0I 1 00 0 0 0 0I 0 0 Is fa function? Justify your answer. That is, if it is a function use the arrow diagram to show it is a...
0.09/1 points Previous Answers SCalcET8 5.3.002. Let g(x)-f(t) dt, where f is the function whose graph is shown (a) Evaluate g(x) for x 0, 1, 2, 3, 4, 5, and 6 g(0)0 9(2)-8 g(3)-( 20 9(4)- 9(5) 9(6) ) g(6)- (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimum x= maximum x= (d) Sketch a rough graph of g. 7 83 gtx ry again....
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...