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...
help with 5 and 6? 5. Find the interval of convergence of .. A) O B) 0 C) (0,00) I D) (-00,00) 6. Which of the following is an equation for the line tangent to the curve x = sin 38 cos , y = sin 30 sin 0 at 0 = */3? A) y = 732 B) y = 3x - C) y=for D) yr yr - 1
(1 point) Suppose that f(x) = (3x + 5). (A) Find an equation for the tangent line to the graph off at x = 2. Tangent line: y = (B) Find the values of a where the tangent line is horizontal. If there are no such values, enter - 1000. Values of x =
Q 4.68a) Find the values of the constants a, b, and c so that the directional derivative of Ф , 2. -1) has a maximum of magnitude 64 in a direction parallel to the z axis. ay + by2+cz, Find the acute angle berween the surfaces y'3x+ and 3x2-y + 2z I at the point (1, -2, 1). Find the constants a and b so that the surface ax -by-(a+2)x will be orthogonal to the surface y+ 4 at the...
32. Simplify : a. x/3-x/4 b. 3/(2x) -4/x c. 1/2x-1/3x 33. Find x if: 3x +6 = 2-5x a. b. x/m + x/n = 1 C 1/x = 3/m d. Sx/3 = 2 34. Find b if: x/(x+a) = 2/b a. b. v(x - b') =y 35. Solve the following Simultaneous linear equations and check in both equations: a) 3x+y=-4 x-2y 1 b) 5x+y=-8 2x-2y 4 Answer: x-1, y.3 36. Evaluate the expression below, if b-3 and c-2. 2bc'+(bc) Helpful...
Find f'(x) f(x) = x х Consider the function f(x) = 5x + x Bx a. Find f'(x) b. Find the x-values where the tangent line is horizontal Use the product rule to differentiate. Do Not Simplify y = (7x4 - x + 2)(x5 + 4)
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...
at x = 2. Question 1. Find the equation of the tangent line to the graph of y = 3x / 2 A) 3x + 2 B) x + 3 C) * +3 D) x + 1 E) x + 2
(a) (6 marks) Determine the values of A, B and C such that 1 x(x 2 + 1) = A x + Bx + C x 2 + 1 . Hence evaluate Z 1 x(x 2 + 1)dx. (b) (6 marks) Find the area under the curve y = xe−x for x ≥ 0. 3. (a) (6 marks) Determine the values of A, B and C such that 1 А + Bir + 12+1 (22+1) 1 Hence evaluate dr. (2+1)...
Question Below are the graphs of f(x)= x²-3x²+1 and x² + y² = 2x²y2 a) Find the equation of the tangent line to the function (on left) at point (-1, f(-1)). 6) Calculate the slope of the tangent line to the function (on right) at point (1,1). 1- . 0,5 1 1.5 1 ST -1,8-1,694 -12 -1 -6.8-06-11-02 BIG 1 112 1,6 10