FIND THE SOLUTION TO THE FOLLOWING INEQUALITY X + 4 = x2 + 2 = 2X + 10 A) (-2,-2) U [4,00) B) (-2,4) C)(-0,-1) U (2.c) D)(-1,2) E)(-0,2] F)(-1,0) G)(-0,–2] U [4,6) H)[-2, -1] [2,4) Select one: a. D b. F C. A d. G e. C f. H g. B h. E
2x f(x) = ex+ f'(x) = (3x + 2) ex+3 B f'(x) = (x2 + 2x) e*+2x-1 С f'(x) = ex®+2x f'(x) = €3x+2
Problem 4. Consider f(x) = x5+ x4 + 2x3 + 3x2 + 4x + 5 ∈ Q[x] and our goal is to determine if f is irreducible over Q. We compute f(1), f(−1), f(5), f(−5) directly and see that none of them is zero. By the Rational Roots Theorem, f has no root in Q. So if f is reducible over Q, it cannot be factored into the product of a linear polynomial and a quartic polynomial (i.e. polynomial of...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
solve each equation algebraically: a) 3+7e^2x=24 b) 2^x+5=7^3x+1 c) 3^(2x) - 3^(x) - 20=0 d) log x + log (x-5)=2 ^6 ^6 e) log(x+2)-log(x-1)=1 f) ln(log (x^2 + 2x))=0 ^3 d og, 71 Solve each of the exponenti a tions call the as well as a decimal approximation to the nearest the get the approximated solutions Yo d ac t o a) 3+72-24 d) 3 -3-20 - 0 get the approximated solution a) loe +log.-5) = 2
3) tx) = x2-2x - 3 A) minimum 1 D) minimum - 4 B) maximum: -4 maximum 1 Use the figure to solve the inequality. 1) f(x) < 0 g(x) = 0 ten ya 8(x) = f(x) A)(x-1<x<2): (-1,2) C) xxs-1 or 2):(--,-1or (2 ) B) x < -1 or 2): --.-1) or (-) D) I-1 sxs 25:-1,21 the western MULTIPLE CHOICE Choose Solve the problem 1) Suppose that ) -- 9 and 4 x - 13. (a) Solve fox)...
(2x - 1 if x < -1 2. Suppose f(x) = 2x2 - 4 if-1<x52 (log: (x - 1) if x > 2 a) Is f continuous at x = -1? Justify your answer completely. b) Is f continuous at x = 22 Justify your answer completely. 3. Suppose f(x) = x2 + 3x a) Using the definition of derivative, find f'(x). No credit will be given if shortcuts are used. b) Find the equation of the tangent line to...
2. For the difference cquation, X2+] = ax, + b = f(x,), where 0 <a < 1 and b> 0, use the solution given in (1.12) to find the following limit: lim ->XX7. Show that this limit is also a fixed point of the difference cquation, that is, it is a solution x of t = f(x) (see Figure 1.2).
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
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)