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QUESTION 1 (25 MARKS) (a) Solve 5+ (3)41 = 12 (6 marks) (b) Find x if...
2. (K/U: 6 marks and T: 6 marks) Solve for x. (a) 2x3 – 3x² – 8x +12<0 o bob UAH (b) log(x + 3) + log(x - 1) – log 21 = 0 (c) 32x+1 < 81
200 In Exercises 12 and 13, find (a) domain, (b) x-intercept and y-intercept, (c) lim f(x), lim f(x), lim f(x) or lim f(x) (if possible), where a is point of discontinuity , (d) Interval of increasing and decreasing, (e) interval of concave up and down, (f) show all extreme and inflection points, and (g) sketch the graph. 12. f(x) = 1 13. f(x) = In()
Find the value x a where the function is discontinuous For the point of discontinuity give (a) f(a) if it exists. (b) limfx). (c) lim f(x), (d) lim 1x), and (e) identify which conditions for continuity Affx) are not met 10 a= (Use a comma to separate answers as needed) (a) Select the choice below and, if necessary, fill in the answer box within your choice O A 8a)= OB. f(a) is undefined (b) Select the choice below and, if...
Please show work on how to solve?
(49. Show that the function (x2 +3 for x < 1 f(x) = 10 - x for 1 < x <2 6x - x2 for x > 2 is continuous for x + 1, 2. Then compute the right- and left-hand lim- its at x = 1, 2, and determine whether f is left-continuous, right- continuous, or continuous at these points (Figure 17). y = 10 - x > 9+ y=6x - x2...
Question 1. Start on a new page. Total marks: 5+6+5+5 = 21. (a) Sketch the natural domain of the function f(x,y) = In (9 - p²-72). Use solid lines for portions of the boundary included in the domain and dashed lines for portions not included. (b) Suppose w = rs'. r = ln(uv)s = re. Use the chain rule, after drawing an appropriate "tree diagramme", to find w/ou in terms of u, v and a (c) Find parametric equations of...
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
Question 6: [12 Marks: 5, 3, 41 Let X1, X2, ..., X6 be a random sample from a population following a Gamma distribution with parameters a and B. Consider the following two estimators of the mean (a/b) of this distribution. Ô2 = X And ôz = ž (X1 + X2 + X3) +ś (X4 + X5 + X3) Where I = (X1 + X2 + ... + X6) (a) Determine the sampling distribution of 7 using moment generating functions. (b)...
can u please solve question 4
4. (10 marks) Find the limit and prove it using the definition. 4x + 13 lim x x²+x+1 sin x if x = 0 if x=0 is differe х 5. (10 marks) Check whether f(x) = proof.
help me to solve this question please
( real analysis )
1. For each of the following use Theorem 3.3.4 to determine if the limit exists and the value of the limit when it does exist. (d) lim 1-40 |+2 (b) lim VH (e) lim / +2 ( limsin Theorem 3.3.4. Suppose f is defined in a deleted neighborhood of a point c. Then lim-f(x) exists and equals Lif and only if both lim + f(x) and lim- f(x) exist...
Use the graph to find the following imits. 6- a. lim f(x)b. lim f(x) x-3 4 2 a. Find f(x) or state that it doesn't exist. Select the correct choice below and fill in any answer boxes lim x→-3 in your choice. -4 -2 OA. f(x)= lim (Type an integer.) O B. The limit does not exist. b. Find lim f(x) or state that it doesn't exist. Select the correct choice below and fill in any answer boxes x→-1 in...