When x2 - 3x + 2k is divided by x +4, the remainder is 21. Find k k= (Simplify your answer.)
21) g(x) 2x-2 f(x)=x2 +3x Find (g f-2+x)
25. (a) Find all2 x 2 matrices whose null space is the line 3x 5y 0 (b) Describe the null spaces of the following matrices: 6 2 0 B A = 0 5 0 3 0
25. (a) Find all2 x 2 matrices whose null space is the line 3x 5y 0 (b) Describe the null spaces of the following matrices: 6 2 0 B A = 0 5 0 3 0
2. Let f(x) = x2+3x-10 x2+x-6 (a) Find the y-intercept. Show all work. (b) Find the x-intercept. Show all work. (c) Find the vertical asymptote(s). Show all work. (d) Find the horizontal asymptote. Explain your solution. (e) Does the rational expression have any holes? Explain.
Find all values x = a where the function is discontinuous. 3x - 5 if x < 0 f(x) = x2 + 5x -5 if x 20 O A. a = 0 OB. Nowhere O c. a = 5 OD. a = -5
Please show all work
Let f(x) = x2 + 3x + 5. a) Find all derivatives of f(x). b) Find the value of f(n) (2) for all derivatives. c). Find the Taylor's series for f(x) centered at c = 2.
7. Find all critical points of the following function. f(x) = 5x3 – x2 – 3x +2 a) x = -1,3 b) x = 2,3 c) x= -2,2 d) None of the above
Consider the following function. f(x) = -½x2 – 3x + 1 Find the slope and an equation of the tangent line to the graph of the function at the point (-2,5). Slope: m= Equation: y = (Enter equation in slope-intercept form, i.e.y = mx + b)
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
21 please
inteb CORE 17 20. The matrices in the last two Exercises were the standard matrices of the operators [proji] and refli], respectively, where L is a line through the origin in R2 with unit direction vector (a, b) See Exercise 25 in Section 2.2. Give a geometric argument as to why one of these matrices is invertible and the other matrix is not invertible. Explain also the geometric significance of the inverse of the invertible matrix. For Exercises...