12. Let m(x)=x2 + 4x + 1 in F5 [x]. Find polynomials f(x),8(x) in Fs [x]...
If two polynomials (2x3 + ax2 + 4x -12) and (x3 + x2 - 2x + a) leave the same remainder when divided by (x - 3) . Find the value of a and also the remainder.
8. Let y = x2 cos x, Find y' 9. Let g(x) = -2 cos x, Find g'(x) 10. Find F(x) = (4x + 3)5, Find F'(x) BONUS QUESTION (15 POINTS Let y = (4x - 3)(x - 1)5; Find y"
A quotient of two polynomials, such as x2 + x x2 ? 4x , is called Incorrect: Your answer is incorrect. expression.
Let CTO,1] 3.(12 pts) Let f=f(x)-mx-1 and g = g have the inner product (x)-4x + m be two functions in q0,1]. Find the exact value(s) of m for which f and g are orthogonal.
Let m(t) = x2 + 3x + 5 in Q[1] and let a(t) = x+ + 4.r3 +5.22 – 67 – 9 and 6(z) = r3 +2.x2 +1. (a) (10 points) Determine whether a c) = (x) (mod m(t)). (b) (10 points) Find the principal representative for b(2) mod m().
5. Is f continuous at f(1)? (10 points) [-x2 +1, 4x, f(x) = -5, -1<x<0 0<x<1 x=1 1<x<3 3<x<5 - 4x + 8 1,
Find the most general antiderivative of f(x) = (3 – 4x) -3 – (1 + x2)-1
Let f=x3 +x2 + x + 1 in Z2 [x]. Write f as a product of irreducible polynomials in Z2 .
Let ?(?)=?2−8?+4f(x)=x2−8x+4. (1 point) Let f(x) = x2 – 8x + 4. Find the critical point c of f(x) and compute f(c). The critical point c is = The value of f(c) = Compute the value of f(x) at the endpoints of the interval [0, 8]. f(0) = f(8) = Determine the min and max Minimum value = Maximum value = Find the extreme values of f(x) on [0, 1]. Minimum value = Maximum value =
Find f −1(x). f(x) = 4x − 8 f −1(x) =