Determine whether p(x) = −x^2 + x + 2 is in span{x^2 + x + 1, 2x^2 + x}. Please explain the steps.
suppose f(x)=x^2+x-6 for x does not equal 2 and f(x)=3 for x=2. Then which of the following statements are true? (I) f(x) is continuous on (-∞, ∞). (II) f(x) is discontinuous at 2 because f(2) is undefined. (III) f(x) is discontinuous at 2 because lim x→2 f(x) does not exist. (IV) f(x) is discontinuous at 2 because lim x→2 f(x) ≠ f(2).
Find an approximation to ex(x)sin(x) for small x. O 1.x-(x 2)/2+(xA3)16 О 2. -(x^2)+(x^3) O 3.x+(x 2)+(x3)2 о 4. xt(x2)+(x^3)/3 O 5.x+(x*2)-(xA3)/6
x²_4 x # 2 x-2, Let f(x) = Which of r = 2 ?the following is true .x = 2 is differentiable at f .x = 2 is continuous at f is is continuous at x = 2 f O x = 2 and has a limit at None of the above o x = 2 has a limit at f O
x^2=2^x find the value of x.
6. Where are the following functions discontinuous? a) f(x) = x+2) x+2 (x+2)x b) f(x) = 21
f(x)=x^2 when x>=0 and f(x)=-x^2 when x <0. find 2f(x)>=f(4-x^2)
2. Solve the initial value problem. -2 2 (1) X"(t) = X, X(0) = 2 -2 0 0 X'(0) = 8 0 0 -1 2 -:] X, X(0) = 0 0 X'(0) 3 0 (2) X"(t) = 1 (3) X"(t) = 1 -6 6 3 -3 ] X X(0) = X(0) = [ 8 ] X'O) = 1 - [8]
2. Let f(x) = -x + 2 and g(x) = (x + 3)2. Determine a simplified algebraic model for each composite function. [K/A-31 a) y = g(f(x)) b) y = f(x) + g(x) d) y=f(x)g(x)
X'=2 -5x, x(x) = -2 z LI -2 5